diff --git a/index.html b/index.html index 1a6cc11..6a5afc3 100644 --- a/index.html +++ b/index.html @@ -1,2 +1,2 @@ - + diff --git a/stable b/stable new file mode 120000 index 0000000..9ff151c --- /dev/null +++ b/stable @@ -0,0 +1 @@ +v0.1.0 \ No newline at end of file diff --git a/v0.1 b/v0.1 new file mode 120000 index 0000000..9ff151c --- /dev/null +++ b/v0.1 @@ -0,0 +1 @@ +v0.1.0 \ No newline at end of file diff --git a/v0.1.0/.documenter-siteinfo.json b/v0.1.0/.documenter-siteinfo.json new file mode 100644 index 0000000..58cf8a5 --- /dev/null +++ b/v0.1.0/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-30T03:49:26","documenter_version":"1.2.1"}} \ No newline at end of file diff --git a/v0.1.0/assets/documenter.js b/v0.1.0/assets/documenter.js new file mode 100644 index 0000000..f531160 --- /dev/null +++ b/v0.1.0/assets/documenter.js @@ -0,0 +1,889 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'minisearch': 'https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function () { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'minisearch'], function($, minisearch) { + +// In general, most search related things will have "search" as a prefix. +// To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +let results = []; +let timer = undefined; + +let data = documenterSearchIndex["docs"].map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; +}); + +// list below is the lunr 2.1.3 list minus the intersect with names(Base) +// (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) +// ideally we'd just filter the original list but it's not available as a variable +const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", +]); + +let index = new minisearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with search results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + boost: { title: 100 }, + fuzzy: 2, + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + } + + return word ?? null; + }, + tokenize: (string) => string.split(/[\s\-\.]+/), + }, +}); + +index.addAll(data); + +let filters = [...new Set(data.map((x) => x.category))]; +var modal_filters = make_modal_body_filters(filters); +var filter_results = []; + +$(document).on("keyup", ".documenter-search-input", function (event) { + // Adding a debounce to prevent disruptions from super-speed typing! + debounce(() => update_search(filter_results), 300); +}); + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + $(this).removeClass("search-filter-selected"); + } else { + $(this).addClass("search-filter-selected"); + } + + // Adding a debounce to prevent disruptions from crazy clicking! + debounce(() => get_filters(), 300); +}); + +/** + * A debounce function, takes a function and an optional timeout in milliseconds + * + * @function callback + * @param {number} timeout + */ +function debounce(callback, timeout = 300) { + clearTimeout(timer); + timer = setTimeout(callback, timeout); +} + +/** + * Make/Update the search component + * + * @param {string[]} selected_filters + */ +function update_search(selected_filters = []) { + let initial_search_body = ` +
Type something to get started!
+ `; + + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + results = index.search(querystring, { + filter: (result) => { + // Filtering results + if (selected_filters.length === 0) { + return result.score >= 1; + } else { + return ( + result.score >= 1 && selected_filters.includes(result.category) + ); + } + }, + }); + + let search_result_container = ``; + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + results.forEach(function (result) { + if (result.location) { + // Checking for duplication of results for the same page + if (!links.includes(result.location)) { + search_results += make_search_result(result, querystring); + count++; + } + + links.push(result.location); + } + }); + + let result_count = `
${count} result(s)
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + filter_results = []; + modal_filters = make_modal_body_filters(filters, filter_results); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(initial_search_body); + } +} + +/** + * Make the modal filter html + * + * @param {string[]} filters + * @param {string[]} selected_filters + * @returns string + */ +function make_modal_body_filters(filters, selected_filters = []) { + let str = ``; + + filters.forEach((val) => { + if (selected_filters.includes(val)) { + str += `${val}`; + } else { + str += `${val}`; + } + }); + + let filter_html = ` +
+ Filters: + ${str} +
+ `; + + return filter_html; +} + +/** + * Make the result component given a minisearch result data object and the value of the search input as queryString. + * To view the result object structure, refer: https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ +function make_search_result(result, querystring) { + let search_divider = `
`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`\\b${querystring}\\b`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`\\b${querystring}\\b`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${result.title}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+
+ ${search_divider} + `; + + return result_div; +} + +/** + * Get selected filters, remake the filter html and lastly update the search modal + */ +function get_filters() { + let ele = $(".search-filters .search-filter-selected").get(); + filter_results = ele.map((x) => $(x).text().toLowerCase()); + modal_filters = make_modal_body_filters(filters, filter_results); + update_search(filter_results); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let search_modal_header = ` + +`; + +let initial_search_body = ` +
Type something to get started!
+`; + +let search_modal_footer = ` + +`; + +$(document.body).append( + ` + + ` +); + +document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); +}); + +document.querySelector(".close-search-modal").addEventListener("click", () => { + closeModal(); +}); + +$(document).on("click", ".search-result-link", function () { + closeModal(); +}); + +document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; +}); + +// Functions to open and close a modal +function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); +} + +function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); +} + +document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v0.1.0/assets/favicon.ico b/v0.1.0/assets/favicon.ico new file mode 100644 index 0000000..542271e Binary files /dev/null and b/v0.1.0/assets/favicon.ico differ diff --git a/v0.1.0/assets/logo-dark.png b/v0.1.0/assets/logo-dark.png new file mode 100644 index 0000000..adda93c Binary files /dev/null and b/v0.1.0/assets/logo-dark.png differ diff --git a/v0.1.0/assets/logo.png b/v0.1.0/assets/logo.png new file mode 100644 index 0000000..9574627 Binary files /dev/null and b/v0.1.0/assets/logo.png differ diff --git a/v0.1.0/assets/preview.png b/v0.1.0/assets/preview.png new file mode 100644 index 0000000..7d6b889 Binary files /dev/null and b/v0.1.0/assets/preview.png differ diff --git a/v0.1.0/assets/themes/documenter-dark.css b/v0.1.0/assets/themes/documenter-dark.css new file mode 100644 index 0000000..9f5449f --- /dev/null +++ b/v0.1.0/assets/themes/documenter-dark.css @@ -0,0 +1,7 @@ +html.theme--documenter-dark .pagination-previous,html.theme--documenter-dark .pagination-next,html.theme--documenter-dark .pagination-link,html.theme--documenter-dark .pagination-ellipsis,html.theme--documenter-dark .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select 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span{font-style:inherit;font-weight:inherit}html.theme--documenter-dark strong{color:#f2f2f2;font-weight:700}html.theme--documenter-dark fieldset{border:none}html.theme--documenter-dark pre{-webkit-overflow-scrolling:touch;background-color:#282f2f;color:#fff;font-size:.875em;overflow-x:auto;padding:1.25rem 1.5rem;white-space:pre;word-wrap:normal}html.theme--documenter-dark pre code{background-color:transparent;color:currentColor;font-size:1em;padding:0}html.theme--documenter-dark table td,html.theme--documenter-dark table th{vertical-align:top}html.theme--documenter-dark table td:not([align]),html.theme--documenter-dark table th:not([align]){text-align:inherit}html.theme--documenter-dark table th{color:#f2f2f2}html.theme--documenter-dark .box{background-color:#343c3d;border-radius:8px;box-shadow:none;color:#fff;display:block;padding:1.25rem}html.theme--documenter-dark a.box:hover,html.theme--documenter-dark a.box:focus{box-shadow:0 0.5em 1em -0.125em rgba(10,10,10,0.1),0 0 0 1px 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.button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-outlined.is-hovered,html.theme--documenter-dark .button.is-black.is-outlined:focus,html.theme--documenter-dark .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark 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.button.is-dark,html.theme--documenter-dark .content kbd.button{background-color:#282f2f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:hover,html.theme--documenter-dark .content kbd.button:hover,html.theme--documenter-dark .button.is-dark.is-hovered,html.theme--documenter-dark .content kbd.button.is-hovered{background-color:#232829;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus,html.theme--documenter-dark .content kbd.button:focus,html.theme--documenter-dark .button.is-dark.is-focused,html.theme--documenter-dark .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-dark:focus:not(:active),html.theme--documenter-dark .content kbd.button:focus:not(:active),html.theme--documenter-dark .button.is-dark.is-focused:not(:active),html.theme--documenter-dark .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(40,47,47,0.25)}html.theme--documenter-dark 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kbd.button.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-dark.is-inverted[disabled],html.theme--documenter-dark .content kbd.button.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-loading::after,html.theme--documenter-dark .content kbd.button.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined,html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-outlined:hover,html.theme--documenter-dark .content kbd.button.is-outlined:hover,html.theme--documenter-dark 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kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-dark.is-outlined[disabled],html.theme--documenter-dark .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined{background-color:transparent;border-color:#282f2f;box-shadow:none;color:#282f2f}html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,html.theme--documenter-dark .content 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kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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.hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/v0.1.0/assets/themeswap.js b/v0.1.0/assets/themeswap.js new file mode 100644 index 0000000..9f5eebe --- /dev/null +++ b/v0.1.0/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/v0.1.0/assets/warner.js b/v0.1.0/assets/warner.js new file mode 100644 index 0000000..3f6f5d0 --- /dev/null +++ b/v0.1.0/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/v0.1.0/base/couplingmodel/index.html b/v0.1.0/base/couplingmodel/index.html new file mode 100644 index 0000000..36a41d7 --- /dev/null +++ b/v0.1.0/base/couplingmodel/index.html @@ -0,0 +1,25 @@ + +CouplingModel · TenNetLib.jl

CouplingModel

TenNetLib.jl degines as struct, called the CouplingModel, to store the Hamiltonian terms. In case of MPS based algorithms, CouplingModel can replace MPO without modifying rest of the code. For Tree Tensor Network (TTN) codes, only CouplingModel can be used. Different elements of CouplingModel are contracted in parallel.

TenNetLib.CouplingModelType
struct CouplingModel{T}
+    sites::Vector{Index{T}}
+    terms::Vector{IDTensors}
+end

CouplingModel for a given OpStrings Hamiltonian terms and sites::Vector{Index}.

  • sites::Vector{Index{T}}: Site Indexs.
  • terms::Vector{IDTensors}: Collection of Hamiltonian terms.
source
TenNetLib.CouplingModelMethod
function CouplingModel(os::OpStrings{T1},
+                       sites::Vector{Index{T2}};
+                       merge::Bool = true,
+                       maxdim::Int = typemax(Int),
+                       mindim::Int = 1,
+                       cutoff::Float64 = Float64_threashold(),
+                       svd_alg::String = "divide_and_conquer",
+                       chunksize::Int = 12) where {T1 <: Number, T2}

Constructor of the CouplingModel from os::OpStrings and sites::Vector{Index}.

Named arguments and their default values:

  • merge::Bool = true. If true, merges all the terms having same spatial support resulting in larger virtual dimension. Otherwise, all the terms have virtual dimension one.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_Threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • chunksize::Int = 12.

Example:

os = OpStrings()    
+for j=1:N-1
+    os += 1, "Sz" => j, "Sz" => j+1
+    os += 0.5, "S+" => j, "S-" => j+1
+    os += 0.5, "S-" => j, "S+" => j+1
+end    
+H = CouplingModel(os,sites)
source
TenNetLib.CouplingModelMethod
function CouplingModel(os::OpStrings{T1},
+                       mpo::MPO;
+                       merge::Bool = true,
+                       maxdim::Int = typemax(Int),
+                       mindim::Int = 1,
+                       cutoff::Float64 = Float64_threashold(),
+                       svd_alg::String = "divide_and_conquer",
+                       chunksize::Int = 12) where {T1 <: Number}

Constructor of the CouplingModel from os::OpStrings and mpo::MPO. Resultant CouplingModel is the sum of os and the mpo.

Named arguments and their default values:

  • merge::Bool = true. If true, merges all the terms having same spatial support resulting in larger virtual dimension. Otherwise, all the terms have virtual dimension one.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_Threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • chunksize::Int = 12.
source
TenNetLib.CouplingModelMethod
function CouplingModel(mpos::MPO...)

Constructs CouplingModel from a collection of MPOs. Different MPO terms are contracted in parallel. Useful for TTN codes.

source
Base.lengthMethod
function Base.length(model::CouplingModel)

Number of sites in the system.

source
Base.copyMethod
function Base.copy(model::CouplingModel)

Shallow copy of CouplingModel.

source
Base.getindexMethod
function Base.getindex(model::CouplingModel, n)

Returns Hamiltonian terms for nth site(s) in the CouplingModel.

source
ITensors.siteindsMethod
function ITensors.siteinds(model::CouplingModel)

Returns the site Indexs of the CouplingModel.

source
diff --git a/v0.1.0/base/fermions/index.html b/v0.1.0/base/fermions/index.html new file mode 100644 index 0000000..f05cde1 --- /dev/null +++ b/v0.1.0/base/fermions/index.html @@ -0,0 +1,3 @@ + +Dealing with Fermions · TenNetLib.jl

Dealing with Fermions

TenNetLib.jl uses the following function to teat fermionic operators.

TenNetLib.bosonizeMethod
function bosonize(oppair::Vector{Pair{String, Int}},
+                  sites::Vector{Index{T}}) where T

Given a string of operator names with positions in the form of Vector{Pair{String, Int}} "bosonizes" the operator string by putting the Jordan-Wigner string "F" at appropriate places.

Arguments

  • oppair::Vector{Pair{String, Int}}: Input string of operator names with positions.
  • sites::Vector{Index}: The entire site Indexs as per ITensors' convention.

Return values

  • ::Int: Even (+1) or odd (-1) permutation.
  • ::Vector{Pair{String, Int}}: modified string of operator names and positions.
source
diff --git a/v0.1.0/base/global/index.html b/v0.1.0/base/global/index.html new file mode 100644 index 0000000..b1d2475 --- /dev/null +++ b/v0.1.0/base/global/index.html @@ -0,0 +1,5 @@ + +Controlling global behaviors · TenNetLib.jl

Controlling global behaviors

TenNetLib.jl provides following functions to control global behaviors for Tensor Network simulations.

TenNetLib.Float64_thresholdFunction
function Float64_threshold()
+function Float64_threshold(threshold::Float)

Returns threshold for floating point calculations. In most places, any number below this will be treated zero. E.g., in cutoff. Default: 1e-15.

Optionally, change the threshold as per the input threshold.

source
TenNetLib.@threaded_loopMacro
macro threaded_loop(code)

Conditional threaded loop by Threads.@threads. If using_threaded_loop() returns true, performs parallel loop, otherwise performs serial loop.

Note: All other forms of parallelization are switched off inside the loop body, if parallel loop is being executed.

Example:

@threaded_loop for i = 1 : N
+    # Do stuff in parallel
+end
source
diff --git a/v0.1.0/base/graph/index.html b/v0.1.0/base/graph/index.html new file mode 100644 index 0000000..81904db --- /dev/null +++ b/v0.1.0/base/graph/index.html @@ -0,0 +1,18 @@ + +The Graph object · TenNetLib.jl

The Graph object

TenNetLib.jl defines its own undirected graph object, the Graph. Currently only used for the Tree Tensor Network (TTN) codes.

TenNetLib.GraphType
mutable struct Graph{T}
+    nodes::Set{T}
+    edges::Dict{T, Set{T}}
+end

Undirected graph where nodes are of type T.

  • nodes::Set{T}: Holds the nodes of the graph.
  • edges::Dict{T, Set{T}}: Holds the edges of the graph. For a given node as key, holds all the connected nodes as value of the Dict.
source
TenNetLib.GraphMethod
function Graph{T}(nodes::Set{T}) where T
+function Graph{T}(nodes::Vector{T}) where T

Constructor of Graph with a list of nodes and empty edges.

  • nodes: Intial nodes.
source
TenNetLib.getnodesMethod
function getnodes(graph::Graph{T}) where T = copy(graph.nodes)

Returns (shallow copy of) nodes in the Graph.

source
TenNetLib.hasnodeMethod
function hasnode(graph::Graph{T}, node::T) where T

Checks whether a node is in the Graph.

source
TenNetLib.addedge!Method
function addedge!(graph::Graph{T}, node1::T, node2::T) where T

Adds an edge between node1 and node2. If node1 or node2 are not present in the Graph, they are added.

source
TenNetLib.isneighborMethod
function isneighbor(graph::Graph{T}, node1::T, node2::T)::Bool where T

Checks whether node1 and node2 are connected by an edge.

source
TenNetLib.bfsMethod
function bfs(graph::Graph{T},
+             source::T,
+             destination::Union{Nothing, T} = nothing) where T

Performs a full BFS starting from the node source (and optionally, to the destination).

Return values

  • ::Dict{T, Int}: Distances of nodes (key) in the BFS path.
  • ::Dict{T, T}: Parents of nodes (key) in the BFS path.
source
TenNetLib.nodes_from_bfsMethod
function nodes_from_bfs(graph::Graph{T}, source::T;
+                        reverse::Bool = false) where T
+
+function nodes_from_bfs(graph::Graph{T}, source::T,
+                        destinations::Union{Set{T}, Vector{T}};
+                        reverse::Bool = false) where T

Returns the Vector of nodes in the BFS path from the source (optionally, towards the destinations). If reverse=true returns the reverse order of nodes.

source
TenNetLib.shortest_pathMethod
function shortest_path(graph::Graph{T}, source::T, destination::T) where T

Returns the shortest path between source and destination in a Graph.

source
TenNetLib.nextnode_in_pathMethod
function nextnode_in_path(graph::Graph{T}, source::T, destination::T, n=1) where T

Returns the next node in the shortest path between source and destination in a Graph. Optionally, finds nth next-node in the path.

source
TenNetLib.has_cycleMethod
function has_cycle(graph::Graph{T}) where T

Checks whether a Graph has cycles/loops in it.

source
TenNetLib.find_sum_central_nodeMethod
function find_sum_central_node(graph::Graph{T}) where T
+function find_sum_central_node(graph::Graph{T}, nodes::Set{T}) where T
+function find_sum_central_node(graph::Graph{T}, nodes::Vector{T}) where T

Finds the sum central node node of a Graph. Optionally, when nodes is specified, finds the central node with respect to the nodes.

source
TenNetLib.find_eccentric_central_nodeMethod
function find_eccentric_central_node(graph::Graph{T}) where T
+function find_eccentric_central_node(graph::Graph{T}, nodes::Set{T}) where T
+function find_eccentric_central_node(graph::Graph{T}, nodes::Vector{T}) where T

Finds the eccentric central node of a Graph. Optionally, when nodes is specified, finds the central node with respect to the nodes.

source
Base.copyMethod
function Base.copy(graph::Graph{T}) where T

Shallow copy of Graph.

source
Base.getindexMethod
function Base.getindex(graph::Graph{T}, node::T) where T

Returns the edges for a given node::T as an index.

source
Base.setindex!Method
function Base.setindex!(graph::Graph{T}, neighbors::Set{T}, node::T) where T
+function Base.setindex!(graph::Graph{T}, neighbors::Vector{T}, node::T) where T

Sets the edges=neighbors for a given node::T as an index.

source
Base.:==Method
function Base.:(==)(graph1::Graph{T}, graph2::Graph{T}) where T

Equality between two Graph objects.

source
diff --git a/v0.1.0/base/misc/index.html b/v0.1.0/base/misc/index.html new file mode 100644 index 0000000..13ae1d3 --- /dev/null +++ b/v0.1.0/base/misc/index.html @@ -0,0 +1,8 @@ + +Miscellaneous typedefs and functions · TenNetLib.jl

Miscellaneous typedefs and functions

TenNetLib.IDTypeType
const IDType = ITensors.IDType

Type of randomly generated id. It is usually UInt64.

source
TenNetLib.IDTensorsType
const IDTensors = Dict{IDType, ITensor}

Dictionary of key = randomly generated id and value = ITensor objects.

source
TenNetLib.combineindsMethod
function combineinds(inds::Vector{Index};
+                     maxdim::Union{Nothing, Int} = nothing, 
+                     maxqnblocks::Union{Nothing, Int} = nothing,
+                     kwargs...)

Combine a vector of Index into one (like ITensors.jl's combiner). maxdim is be the maximum dimension of the output Index, maxqnblocks represents maximum number of QN blocks to retain in the output Index.

source
TenNetLib.indexintersectionMethod
function indexintersection(inds1::Vector{Index}, inds2::Vector{Index};
+                           maxdim::Union{Nothing, Int} = nothing,
+                           maxqnblocks::Union{Nothing, Int} = nothing,
+                           kwargs...)

Performs set intersection of two vectors of Index. maxdim is be the maximum dimension of the output Index, maxqnblocks represents maximum number of QN blocks to retain in the output Index.

source
diff --git a/v0.1.0/base/opstrings/index.html b/v0.1.0/base/opstrings/index.html new file mode 100644 index 0000000..00ede97 --- /dev/null +++ b/v0.1.0/base/opstrings/index.html @@ -0,0 +1,19 @@ + +OpStrings · TenNetLib.jl

OpStrings

TenNetLib.jl provides an alternative, called OpStrings, to ITensors.jl's OpSum to automatically construct Hamiltonains / operators. TenNetLib.jl's own CouplingModel is built from OpStrings and is not compatible with OpSum.

OpString

OpStrings is basically a vector of OpString objects (notice the difference in 's' at the end)

TenNetLib.OpStringType
struct OpString{T <: Number}
+    coeff::T
+    ops::Vector{Pair{String, Int}}
+end

Holds operator strings (operator names with corresponding positions) along with the coefficient.

  • coeff::T: Coeffcient of the operator string.
  • ops::Vector{Pair{String, Int}}: String of operator names along with the positions.
source
TenNetLib.minsiteMethod
function minsite(opstr::OpString)

Returns the lowest site position in the operator string of the OpString.

source
TenNetLib.maxsiteMethod
function maxsite(opstr::OpString)

Returns the highest site position in the operator string of the OpString.

source
TenNetLib.removeIdsMethod
function removeIds(opstr::OpString{T}) where {T <: Number}

Returns an OpString with all "Id" operators removed from the original.

source
TenNetLib.bosonizeMethod
function bosonize(opstr::OpString{T1},
+                  sites::Vector{Index{T2}}) where {T1 <: Number, T2}

Returns an OpString after "bosonizing" the original with Jordan-Wigner strings as needed. See bosonize.

source

OpStrings

TenNetLib.OpStringsType
const OpStrings{T} = Vector{OpString{T}}

Collection of OpStrings.

Syntax:

os = OpStrings()
+os += 1, "Sx" => i, "Sx" => j, "Sx" => k, ....
+os += "Sx" => i, "Sx" => j, "Sx" => k, ....

Example:

os = OpStrings()    
+for j=1:N-1
+    os += 1, "Sz" => j, "Sz" => j+1
+    os += 0.5, "S+" => j, "S-" => j+1
+    os += 0.5, "S-" => j, "S+" => j+1
+end
source
TenNetLib.removeIdsZerosMethod
function removeIdsZeros(os::OpStrings{T}) where {T <: Number}

Returns an OpStrings with all "Id" operators removed from the original, as well as any OpString term that has coeff less than Float64_threshold().

source
TenNetLib.bosonizeMethod
function bosonize(os::OpStrings{T1}, sites::Vector{Index{T2}}) where {T1 <: Number, T2}

Returns an OpStrings after "bosonizing" the original with Jordan-Wigner strings as needed. See bosonize.

source
TenNetLib.mergetermsMethod
function mergeterms(os::OpStrings{T}) where T <: Number

Returns an OpStrings where OpString elements with exactly same operator strings has been merged by adding the coefficients.

source

MPO from OpStrings

ITensors.MPOMethod
function ITensors.MPO(os::OpStrings{T1},
+                      sites::Vector{Index{T2}};
+                      maxdim::Int = typemax(Int),
+                      mindim::Int = 1,
+                      cutoff::Float64 = Float64_threashold(),
+                      svd_alg::String = "divide_and_conquer",
+                      chunksize::Int = 12) where {T1 <: Number, T2}

Creates MPO from os::OpStrings. The present version uses recursive SVDs to create the MPO. Very inefficient when number of Hamiltonian terms is large. Future updates will solve the problem.

Named arguments and their default values:

  • maxdim::Int = typemax(Int): Maximum MPO bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum MPO bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • chunksize::Int = 12. Maximum size of the chunks on which recursive SVDs are performed.
source
diff --git a/v0.1.0/base/solver/index.html b/v0.1.0/base/solver/index.html new file mode 100644 index 0000000..e0045cf --- /dev/null +++ b/v0.1.0/base/solver/index.html @@ -0,0 +1,2 @@ + +Solvers · TenNetLib.jl

Solvers

Functions to perform local updates. These functions use Krylovkit.jl.

TenNetLib.eig_solverFunction
function eig_solver(env, phi0::ITensor, time_step::Nothing; kwargs...)

Solver to find smallest eigenvalue corresponding to "matrix" env and input vector phi0.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true
  • solver_tol::Float64 = 1E-14.
  • solver_krylovdim::Int = 5.
  • solver_maxiter::Int = 2.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false.
  • solver_check_convergence::Bool = false.

Return values:

  • ::Float64: Smallest eigenvalue.
  • ::ITensor: Eigenstate corresponding to the smallest eigenvalue.
source
TenNetLib.exp_solverFunction
function exp_solver(env, phi0::ITensor, time_step::Union{Float64, ComplexF64}; kwargs...)

Exponentiation solver to find exp(env * phi0 * time_step).

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true
  • solver_tol::Float64 = 1E-12.
  • solver_krylovdim::Int = 30.
  • solver_maxiter::Int = 10.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = true.
  • solver_check_convergence::Bool = true.

Return values:

  • ::Float64: NaN.
  • ::ITensor: Exponentiated ITensor.
source
diff --git a/v0.1.0/index.html b/v0.1.0/index.html new file mode 100644 index 0000000..d7b099f --- /dev/null +++ b/v0.1.0/index.html @@ -0,0 +1,89 @@ + +Introduction · TenNetLib.jl

TenNetLib.jl

A Tensor Network Library (TenNetLib.jl) built on top of ITensors.jl for quantum many-body problems.

Build StatusDocumentation
Build StatusBuild Status

The source code for TenNetLib.jl can be found on GitHub

The documentation for TenNetLib.jl can be found here.

This library requires Julia 1.7+.

Overview

TenNetLib.jl features widely-used Tensor Network (TN) codes, designed with a multi-layered abstraction to cater to diverse user needs. The library provides users with varying levels of control over their computations. Currently, TenNetLib.jl presents an array of functionalities for:

  • (a) Finite-size Matrix-Product States (MPS): Different variants of Density Matrix Renormalization Group (DMRG) and Time Dependent Variational Principle (TDVP) (including subspace expansion) methods.
  • (b) Tree Tensor Network (TTN): Variational search for the ground state and first few excited states.

Installation

TenNetLib.jl is registered on Julia General Registry. To install the library (along with ITensors.jl), you can use the following steps:

$ julia
+
+julia> ]
+
+pkg> add ITensors
+
+pkg> add TenNetLib

Found an issue or bug?

"Beware of bugs in the above code; I have only proved it correct, not tried it." – Donald Knuth

If you find bugs or a mistakes of any kind, please let us know by adding an issue to the GitHub issue tracker. You are also welcome to submit a pull request.

Future functionality?

Here is a list for future additions in the decreasing order of priority. Any help / suggestion is welcome.

  • Augmented Tree Tensor Network (aTTN) for variational ground state search for 2D problems.
  • Infinite DMRG (iDMRG) and/or Variational Uniform Matrix Product States (VUMPS) to tackle 1D / quasi-1D problems directly at the thermodynamic limit.
  • Projected Entangled Pair States (PEPS) for 2D problems.
  • Real-time evolution method using PEPS and TTN.

Also, please feel free to ask about a new feature by adding a new request to the GitHub issue tracker labelled feature request. Note that submitting a pull request, providing the needed changes to introduced your requested feature, will speed up the process.

Example: A simple DMRG code

The following code is for a simple DMRG run at the highest level of abstraction without any additional control.

using ITensors
+using TenNetLib
+
+let
+    N = 32
+    sites = siteinds("S=1/2",N)
+    os = OpSum()
+    
+    for j=1:N-1
+        os += 1, "Sz", j,"Sz", j+1
+        os += 0.5, "S+", j, "S-", j+1
+        os += 0.5, "S-", j, "S+", j+1
+    end
+    
+    H = MPO(os,sites)
+    states = [isodd(n) ? "Up" : "Dn" for n in 1:N]
+    psi0 = MPS(sites, states)
+
+    params = DMRGParams(;nsweeps = [5, 5], maxdim = [20, 50],
+                        cutoff = 1e-14, noise = 1e-3, noisedecay = 2,
+                        disable_noise_after = 3)
+
+    # dmrg2 for two-site DMRG
+    en, psi = dmrg2(psi0, H, params)
+end

Example: A simple TDVP code

The following code is for a simple TDVP run at the highest level of abstraction without any additional control.

using ITensors
+using TenNetLib
+
+let
+    N = 32
+    sites = siteinds("S=1/2",N)
+    os = OpSum()
+    
+    for j=1:N-1
+        os += 1, "Sz", j,"Sz", j+1
+        os += 0.5, "S+", j, "S-", j+1
+        os += 0.5, "S-", j, "S+", j+1
+    end
+    
+    H = MPO(os,sites)
+    states = [isodd(n) ? "Up" : "Dn" for n in 1:N]
+    psi0 = MPS(sites, states)
+
+    tau = -0.01im    
+    engine = TDVPEngine(psi0, H)
+    for ii = 1:100
+
+    	# `nsite = "dynamic"` for dynamical selection between
+	# single- and two-site variants at different bonds
+        tdvpsweep!(engine, tau,
+                   nsite = "dynamic";
+                   maxdim = 200,
+                   cutoff = 1E-12,
+                   extendat = 5)
+
+	psi = getpsi(engine)
+	# DO STUFF
+    end
+end

Example: A simple TTN ground-state optimzation code

The following code is for a simple TTN ground-state optimzation run at the highest level of abstraction without any additional control. Here we use OpStrings and CouplingModel instead of OpSum and MPO.

using ITensors
+using TenNetLib
+
+let
+    N = 32
+    sites = siteinds("S=1/2",N)
+    os = OpStrings()
+    
+    for j=1:N-1
+        os += 1, "Sz" => j,"Sz" => j+1
+        os += 0.5, "S+" => j, "S-" => j+1
+        os += 0.5, "S-"=> j, "S+" => j+1
+    end
+    
+    H = CouplingModel(os,sites)
+    psi0 = TTN(sites, 64, QN("Sz", 0))
+
+    sweeppath = default_sweeppath(psi0)
+    
+    params = OptimizeParamsTTN(; maxdim = [64, 128], nsweeps = [5, 10], 
+                               cutoff = 1e-14, noise = 1e-2, noisedecay = 5, 
+                               disable_noise_after = 5)
+			       
+    en, psi = optimize(psi0, H, params, sweeppath)
+end

diff --git a/v0.1.0/mps/dmrg/index.html b/v0.1.0/mps/dmrg/index.html new file mode 100644 index 0000000..233ebd6 --- /dev/null +++ b/v0.1.0/mps/dmrg/index.html @@ -0,0 +1,23 @@ + +Performing DMRG · TenNetLib.jl

Performing DMRG

Functions to perfom (and control) DMRG runs.

DMRGParams

TenNetLib.jl defines a struct, called DMRGParams, to control DMRG simulations.

TenNetLib.DMRGParamsType
mutable struct DMRGParams
+    maxdim::Vector{Int}
+    nsweeps::Vector{Int}
+    cutoff::Vector{Float64}
+    noise::Vector{Float64}
+    noisedecay::Vector{Float64}
+    disable_noise_after::Vector{Int}
+end

Holds parameters to control DMRG sweeps.

  • maxdim::Vector{Int}: Maximum allowed MPS bond/link dimensions at each stages of DMRG.
  • nsweeps::Vector{Int}: Number of sweeps to be performed at each statges of DMRG.
  • cutoff::Vector{Float64}: Cutoff for SVD truncation at each stages of DMRG.
  • noise::Vector{Float64}: Noise level at each stages of DMRG.
  • noisedecay::Vector{Float64}: Decay of noise level at each states of DMRG. Noise is divided by noisedecay after each sweep.
  • disable_noise_after::Vector{Int}: Switch of noise after this many sweeps at each

states of DMRG.

All these Vectors must have same dimension.

source
TenNetLib.DMRGParamsMethod
function DMRGParams(;maxdim::Vector{Int}, nsweeps::Vector{Int}, 
+                    cutoff::Union{Vector{Float64}, Float64} = _Float64_Threshold,
+                    noise::Union{Vector{Float64}, Float64, Int} = 0.0,
+                    noisedecay::Union{Vector{Float64}, Float64, Int} = 1.0,
+                    disable_noise_after::Union{Vector{Int}, Int} = typemax(Int))

Constructor for DMRGParams. Takes only named arguments.

  • maxdim::Vector{Int}: Maximum allowed MPS bond/link dimensions at each stages of DMRG.
  • nsweeps::Vector{Int}: Number of sweeps to be performed at each statges of DMRG.
  • cutoff::Union{Float64, Vector{Float64}} = Float64_threshold(): Cutoff for SVD truncation at each stages of DMRG. If Float64, cutoff remains same throughout the DMRG simulation.
  • noise::Union{Float64, Int, Vector{Float64}} = 0.0: Noise level at each stages of DMRG. If Float64 or Int, initial noise remains same throughout the DMRG simulation.
  • noisedecay::Union{Float64, Int, Vector{Float64}} = 1.0: Decay of noise level at each states of DMRG. Noise is divided by noisedecay after each sweep. If Float64 or Int, noisedecay remains same throughout the DMRG simulation.
  • disable_noise_after::Union{Int, Vector{Int}} = typemax(Int): Switch of noise after this many sweeps at each states of DMRG. If Int, disable_noise_after remains same throughout the DMRG simulation.
source
Base.copyMethod
Base.copy(params::DMRGParams)

Shallow copy DMRGParams.

source

A lower level DMRG function

Following function modifies StateEnvs in-place. Skip this function if you want to avoid lower-level abstraction.

TenNetLib.dmrg!Method
function dmrg!(sysenv::StateEnvs, params::DMRGParams, nsite::Int; kwargs...)

Performs DMRG.

Arguments:

  • sysenv::StateEnvs.
  • params::DMRGParams.
  • nsite::Int of the environment. Either 1 or 2 for one-site or two-site update respectively.

Named arguments and their default values:

  • normalize::Bool = true: Whether to normalize after update.
  • svd_alg::String = "divide_and_conquer".
  • weight::Float64 = -1.0: Weight for the excited state DMRG. Must be set to greater than 0 for the excited state DMRG.
  • outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Convergence criteria:

  • energyErrGoal: DMRG (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.
  • entropyErrGoal: DMRG (at a particluar stage) stops when mid-chain entropy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.

When both energyErrGoal and entropyErrGoal are given, both conditions must be satisfied to trigger this early stopping.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true.
  • solver_tol::Float64 = 1E-14.
  • solver_krylovdim::Int = 5.
  • solver_maxiter::Int = 2.
  • solver_outputlevel::Int = 0.: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false.
  • solver_check_convergence::Bool = false.

Return values:

  • SweepData
source

Higher level DMRG functions

Standard two- and single-site DMRG functions. Single-site DMRG can increasing the bond-dimension if noise > Float64_threshold().

TenNetLib.dmrg2Method
function dmrg2(psi0::MPS, H::MPO, params::DMRGParams; kwargs...)
+function dmrg2(psi0::MPS, H::CouplingModel, params::DMRGParams; kwargs...)
+function dmrg2(psi0::MPS, Hs::Vector{MPO}, params::DMRGParams; kwargs...)
+function dmrg2(psi0::MPS, H::MPO, Ms::Vector{MPS}, params::DMRGParams; kwargs...)
+function dmrg2(psi0::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}, params::DMRGParams; kwargs...)
+function dmrg2(psi0::MPS, H::CouplingModel, Ms::Vector{MPS}, params::DMRGParams; kwargs...)

Performs two-site DMRG.

Arguments:

  • psi0::MPS: Initial MPS.
  • H::MPO, H::CouplingModel, Hs::Vector{MPO}, Ms::Vector{MPS}.
  • params::DMRGParams.

Named arguments and their default values:

  • normalize::Bool = true: Whether to normalize after update.
  • svd_alg::String = "divide_and_conquer".
  • weight::Float64 = -1.0: Weight for the excited state DMRG. Must be set to greater than 0 for the excited state DMRG.
  • outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Convergence criteria:

  • energyErrGoal: DMRG (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.
  • entropyErrGoal: DMRG (at a particluar stage) stops when mid-chain entropy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.

When both energyErrGoal and entropyErrGoal are given, both conditions must be satisfied to trigger this early stopping.

Named arguments for eig_solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true.
  • solver_tol::Float64 = 1E-14.
  • solver_krylovdim::Int = 5.
  • solver_maxiter::Int = 2.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false.
  • solver_check_convergence::Bool = false.

Return values:

  • ::Float64: Energy.
  • ::MPS: The state psi.
source
TenNetLib.dmrg1Method
function dmrg1(psi0::MPS, H::MPO, params::DMRGParams; kwargs...)
+function dmrg1(psi0::MPS, H::CouplingModel, params::DMRGParams; kwargs...)
+function dmrg1(psi0::MPS, Hs::Vector{MPO}, params::DMRGParams; kwargs...)
+function dmrg1(psi0::MPS, H::MPO, Ms::Vector{MPS}, params::DMRGParams; kwargs...)
+function dmrg1(psi0::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}, params::DMRGParams; kwargs...)
+function dmrg1(psi0::MPS, H::CouplingModel, Ms::Vector{MPS}, params::DMRGParams; kwargs...)

Performs single-site DMRG. All other details are same as in dmrg2.

source
diff --git a/v0.1.0/mps/example_dmrg/index.html b/v0.1.0/mps/example_dmrg/index.html new file mode 100644 index 0000000..e04e35f --- /dev/null +++ b/v0.1.0/mps/example_dmrg/index.html @@ -0,0 +1,74 @@ + +Example: DMRG · TenNetLib.jl

Example: DMRG

A straight-forward DMRG can be performed as follows.

using ITensors
+using TenNetLib
+
+let
+    N = 32
+    sites = siteinds("S=1/2",N)
+    os = OpStrings()
+    
+    for j=1:N-1
+        os += 1, "Sz" => j, "Sz" => j+1
+        os += 0.5, "S+" => j, "S-" => j+1
+        os += 0.5, "S-" => j, "S+" => j+1
+    end
+    
+    H = CouplingModel(os,sites)
+    states = [isodd(n) ? "Up" : "Dn" for n in 1:N]
+    psi0 = MPS(sites, states)
+
+    params = DMRGParams(;nsweeps = [10, 10], maxdim = [20, 50],
+                        cutoff = 1e-14, noise = 1e-3, noisedecay = 2,
+                        disable_noise_after = 5)
+
+    # dmrg2 for two-site DMRG
+    en, psi = dmrg2(psi0, H, params)
+
+    # or dmrg1 for single-site DMRG
+    # en, psi = dmrg1(psi0, H, params)
+end

Here, we have used OpStrings and CouplingModel. Alternatively, standard OpSum and MPO can be used.

Instead of using such higher-level code, one can also use lower-level functions for a better control.

sysenv = StateEnvs(psi0, H)
+nsite = 2 # two-site update
+
+swdata = dmrg!(sysenv, params, nsite)
+
+# Get energy from `Sweepdata`
+energy = swdata.energy[end]
+
+# take a shallow copy of the MPS
+# if the `StateEnvs` will be updated later again
+psi = getpsi(sysenv)
+
+# Alternatively, take the psi from `StateEnvs` itself.
+# NOTE: This can crash the simulation, if the MPS is modified (e.g., in measurements)
+# and `StateEnvs` is going to be updated later on.
+# psi = sysenv.psi

Most often, it is better to do a single-site DMRG (without any noise) after standard two-site update for better convergence. Such lower-level function using StateEnvs is useful for that.

sysenv = StateEnvs(psi0, H)
+
+params2 = DMRGParams(;nsweeps = [10, 10], maxdim = [20, 50],
+                     cutoff = 1e-14, noise = 1e-3, noisedecay = 2,
+                     disable_noise_after = 5)
+dmrg!(sysenv, params2, 2)
+
+params1 = DMRGParams(;nsweeps = [10], maxdim = [50], cutoff = 0.0)
+dmrg!(sysenv, params1, 1)

Using such lower-level function, one can also restart the simulation at later times (e.g., by saving the StateEnvs using Serialization.jl), or one can perform updateH! to slowly change the Hamiltonian during DMRG simulations. Most often it is better to perform a

Global Subspace Expansion can also be used to get rid of nasty local minimas (if needed), if the StateEnvs is built from a single MPO.

krylov_extend!(sysenv; extension_applyH_maxdim = 40)
Warning

Global Subspace Expansion may result into huge MPS bond dimension. That is why the named input parameters of krylov_extend! should be chosen carefully.

Excited state DMRG

Excited state DMRG is also straightforword.

# Given a ground state `psi_gr`, initial MPS `psi0`,
+# and a Hamiltonian `H`
+
+# dmrg2 for two-site DMRG
+en, psi = dmrg2(psi0, H, [psi_gr], params; weight = 10.0)
+
+# or dmrg1 for single-site DMRG
+# en, psi = dmrg1(psi0, H, [psi_gr], params; weight = 10.0)

Similarly, using StateEnvs:

sysenv_ex = StateEnvs(psi0, H, [psi_gr]; weight = 10.0)
+nsite = 2 # two-site update
+
+swdata_ex = dmrg!(sysenv_ex, params, nsite)
+
+# Get energy from `Sweepdata`
+energy1 = swdata_ex.energy[end]
+
+# take a shallow copy of the MPS
+# if the `StateEnvs` will be updated later again
+psi1 = getpsi(sysenv_ex)
+
+# Alternatively, take the psi from `StateEnvs` itself.
+# NOTE: This can crash the simulation, if the MPS is modified (e.g., in measurements)
+# and `StateEnvs` is going to be updated later.
+# psi1 = sysenv_ex.psi
diff --git a/v0.1.0/mps/example_tdvp/index.html b/v0.1.0/mps/example_tdvp/index.html new file mode 100644 index 0000000..19feccb --- /dev/null +++ b/v0.1.0/mps/example_tdvp/index.html @@ -0,0 +1,112 @@ + +Example: TDVP · TenNetLib.jl

Example: TDVP

Time-evolution with time dependent variational principle (TDVP).

A straight-forward TDVP (with dynamical sweeps) can be performed as follows. Note that TDVP computes ψ' = exp(time_step * H) * ψ. Therefore, for real-time dynamics with step dt, time_step should be -im * dt.

using ITensors
+using TenNetLib
+
+let
+    N = 32
+    sites = siteinds("S=1/2",N)
+    os = OpSum()
+    
+    for j=1:N-1
+        os += 1, "Sz", j, "Sz", j+1
+        os += 0.5, "S+", j, "S-", j+1
+        os += 0.5, "S-", j, "S+", j+1
+    end
+    
+    H = MPO(os,sites)
+    states = [isodd(n) ? "Up" : "Dn" for n in 1:N]
+    psi0 = MPS(sites, states)
+
+    tau = -0.01im    
+    engine = TDVPEngine(psi0, H)
+    for ii = 1:100
+
+    	# `nsite = "dynamic"` for dynamical selection between
+	# single- and two-site variants at different bonds
+        tdvpsweep!(engine, tau,
+                   nsite = "dynamic";
+                   maxdim = 200,
+                   cutoff = 1E-12,
+                   extendat = 5)
+
+	# Errors in the last sweep and the total error till this point
+	swerr = sweeperror(engine)
+	totalerr = totalerror(engine)
+	
+	psi = getpsi(engine)
+	
+	# DO STUFF
+    end
+end

Here, we have used OpSum and MPO. Alternatively, standard OpStrings and CouplingModel can be used.

Optionally, one can use pure single- or two-site updates. If the TDVPEngine is created with a single MPO then Global Subspace Expansion can be performed.

for ii = 1:100
+
+    # GSE at every 5th sweep.
+    if ii % 5 == 1
+        krylov_extend!(engine)
+    end
+    
+    # `nsite = 1` for single-site update
+    tdvpsweep!(engine, tau,
+               nsite = 1;
+               maxdim = 200,
+               cutoff = 1E-12)
+
+    # Errors in the last sweep and the total error till this point
+    swerr = sweeperror(engine)
+    totalerr = totalerror(engine)
+	
+    psi = getpsi(engine)
+	
+    # DO STUFF
+end

Time-evolution with time-dependent Hamiltonian

For time-dependent Hamiltonian, updateH! can be used.

using ITensors
+using TenNetLib
+
+function makeHt(sites, t)
+
+    os = OpSum()    
+    for j=1:N-1
+        os += 1, "Sz", j, "Sz", j+1
+        os += 0.5, "S+", j, "S-", j+1
+        os += 0.5, "S-", j, "S+", j+1
+    end
+    for j=1:N
+        os += t, "Sz", j
+    end
+    return MPO(os,sites)
+end
+
+let
+    N = 32
+    sites = siteinds("S=1/2",N)
+
+    states = [isodd(n) ? "Up" : "Dn" for n in 1:N]
+    psi0 = MPS(sites, states)
+
+    dt = 0.01
+    tau = -im * dt
+
+    H0 = makeHt(sites, 0.0)
+    engine = TDVPEngine(psi0, H0)
+    
+    for ii = 1:100
+
+    	# `nsite = "dynamic"` for dynamical selection between
+	# single- and two-site variants at different bonds
+        tdvpsweep!(engine, tau,
+                   nsite = "dynamic";
+                   maxdim = 200,
+                   cutoff = 1E-12,
+                   extendat = 5)
+
+	# Errors in the last sweep and the total error till this point
+	swerr = sweeperror(engine)
+	totalerr = totalerror(engine)
+	
+	psi = getpsi(engine)
+	
+	# DO STUFF
+
+	# update Hamiltonian for the next iteration
+	Ht = makeHt(sites, ii*dt)
+	updateH!(engine, Ht)
+    end
+end

Note 1: The above example for time-dependent Hamiltonian is very crude. In real situations, the update in the Hamiltonian should be done with proper care.

Note 2: When the TDVPEngine is created from a single MPO and dt is small, one can use recalcEnv = false in updateH!, so that environments from the last step is reused.

diff --git a/v0.1.0/mps/measure/index.html b/v0.1.0/mps/measure/index.html new file mode 100644 index 0000000..628c2f7 --- /dev/null +++ b/v0.1.0/mps/measure/index.html @@ -0,0 +1,4 @@ + +Measuring the MPS · TenNetLib.jl

Measuring the MPS

TenNetLib.entropyMethod
function entropy(psi::MPS, bond::Int)

Compute von Neumann Entropy of a given MPS psi at bond.

source
TenNetLib.entropyMethod
function entropy(psi::MPS; kwargs...)

Compute von Neumann Entropies of a given MPS psi at all the bonds.

Optionally, for specific bonds, keyword argument bonds can be specified, e.g., bonds = [1, 2, 3].

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::MPS, opten::ITensor)

Returns (complex / real) local expectation value (::ComplexF64 / ::Float64) of a given MPS psi::MPS. The operator opten::ITensor must be single-site operator.

For ElT = Float64, if the expectation value is complex, raises a warning!

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::MPS, opstr::String, pos::Int)

Returns (complex / real) local expectation value (::ComplexF64 / ::Float64) of a given MPS psi::MPS for a given operator name (opstr::String) and a site index (pos::Int)

For ElT = Float64, if the expectation value is complex, raises a warning!

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::MPS, opstr::String; kwargs...)

Returns (complex / real) local expectation values (::Vector{ComplexF64} / ::Vector{Float64}) of a given MPS psi::MPS for a given operator name (opstr::String) at all the sites.

Optionally, for specific sites, keyword argument sites can be specified, e.g., sites = [1, 2, 3].

For ElT = Float64, if the expectation value is complex, raises a warning!

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::MPS, optens::Vector{ITensor})

Returns (complex / real) multi-site expectation value (::ComplexF64 / ::Float64) of a given MPS psi::MPS for a given vector of single-site operators (optens::Vector{ITensor}).

For ElT = Float64, if the expectation value is complex, raises a warning!

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::MPS, oppairs::Vector{Pair{String, Int}};
+                 isfermions::Bool = true)

Returns (complex / real) multi-site expectation value (::ComplexF64 / ::Float64) of a given MPS psi::MPS. oppairs::Vector{Pair{String, Int}} contains pairs of operator names (String) and site locations (Int). E.g., for <ψ|OᵢOⱼOₖ... |ψ>, oppairs = ["O" => i, "O" => j, "O" => k,...].

Fermionic JW strings are added automatically for fermionic operators if isfermions::Bool = true (default).

For ElT = Float64, if the expectation value is complex, raises a warning!

Example:

valueC = measure(psi, ["Cdag" => 2, "C" => 6, "Cdag" => 9, "C" => 12])
+valueR = measure(Float64, psi, ["Cdag" => 2, "C" => 6, "Cdag" => 9, "C" => 12])
source
diff --git a/v0.1.0/mps/state_envs/index.html b/v0.1.0/mps/state_envs/index.html new file mode 100644 index 0000000..db58420 --- /dev/null +++ b/v0.1.0/mps/state_envs/index.html @@ -0,0 +1,14 @@ + +StateEnvs · TenNetLib.jl

StateEnvs: A container to store the MPS and its environments

At the lowest-level of abstraction, TenNetLib.jl defines StateEnvs to hold an MPS and its environments to be modified in place.

Skip this part if you want to avoid lower-level abstraction.

TenNetLib.StateEnvsType
mutable struct StateEnvs{T <: Union{ProjMPO,
+                              ProjMPO_MPS2,
+                              ProjMPOSum2,
+                              ProjMPOSum_MPS,
+                              ProjCouplingModel,
+                              ProjCouplingModel_MPS}
+                        }
+    psi::MPS
+    PH::T
+end

Holds the MPS state psi and its environments PH.

source
TenNetLib.getenvMethod
function getenv(sysenv::StateEnvs)

Returns (shallow copy of) the environment PH.

source
TenNetLib.StateEnvsMethod
function StateEnvs(psi::MPS, Hs::Vector{MPO})

Constructor of the StateEnvs from a vector of MPO. Environments are contracted in parallel.

source
TenNetLib.StateEnvsMethod
function StateEnvs(psi::MPS, H::MPO, Ms::Vector{MPS}; weight::Float64)

Constructor of the StateEnvs from a single MPO and a vector of MPS used for excited state DMRG.

source
TenNetLib.StateEnvsMethod
function StateEnvs(psi::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}; weight::Float64)

Constructor of the StateEnvs from a vector of MPO and a vector of MPS used for excited state DMRG. Environments for MPOs are contracted in parallel.

source
TenNetLib.StateEnvsMethod
function StateEnvs(psi::MPS, H::CouplingModel)

Constructor of the StateEnvs from a CouplingModel. Each terms in the CouplingModel are contracted in parallel.

source
TenNetLib.StateEnvsMethod
function StateEnvs(psi::MPS, H::CouplingModel, Ms::Vector{MPS}; weight::Float64)

Constructor of StateEnvs from a CouplingModel and a vector of MPS used for excited state DMRG. Each terms in the CouplingModel are contracted in parallel.

source
TenNetLib.updateH!Method
function updateH!(sysenv::StateEnvs{ProjMPO}, H::MPO; recalcEnv::Bool = true)

Update Hamiltonian H in sysenv::StateEnvs. If recalcEnv = false, it reuses previous environments.

source
TenNetLib.updateH!Method
function updateH!(sysenv::StateEnvs{ProjMPOSum2}, Hs::Vector{MPO}; recalcEnv::Bool = true)

Update Hamiltonian H in sysenv::StateEnvs. recalcEnv = false is not supported.

source
TenNetLib.updateH!Method
function updateH!(sysenv::StateEnvs{ProjMPO_MPS2}, H::MPO, Ms::Vector{MPS};
+                  weight::Float64, recalcEnv::Bool = true)

Update Hamiltonian H in sysenv::StateEnvs. recalcEnv = false is not supported.

  • weight::Union{Nothing, Float64} = nothing.
source
TenNetLib.updateH!Method
function updateH!(sysenv::StateEnvs{ProjMPOSum_MPS}, Hs::Vector{MPO}, Ms::Vector{MPS};
+                  weight::Float64, recalcEnv::Bool = true)

Update Hamiltonian H in sysenv::StateEnvs. recalcEnv = false is not supported.

  • weight::Union{Nothing, Float64} = nothing.
source
TenNetLib.updateH!Method
function updateH!(sysenv::StateEnvs{ProjCouplingModel_MPS}, H::CouplingModel, Ms::Vector{MPS};
+                  weight::Float64, recalcEnv::Bool = true)

Update Hamiltonian H in sysenv::StateEnvs. recalcEnv = false is not supported.

  • weight::Union{Nothing, Float64} = nothing.
source
ITensors.nsiteMethod
function nsite(sysenv::StateEnvs)

Returns the nsite of the environment. nsite = 1 for single-site environment, nsite = 2 for two-site environmrnt, and so on. Currently, only uses nsite = 0, 1, or 2.

source
ITensors.set_nsite!Method
function set_nsite!(sysenv::StateEnvs, nsite::Int)

Set nsite of the environment. nsite = 1 for single-site environment, nsite = 2 for two-site environmrnt, and so on. Currently, only uses nsite = 0, 1, or 2.

source
ITensors.position!Method
function position!(sysenv::StateEnvs, pos::Int)

Compute the left and right environments at position pos.

source
TenNetLib.productMethod
function product(sysenv::StateEnvs, v::ITensor)

Returns the Matrix-Vector product between the environment and input ITensor v.

source
Base.copyMethod
function Base.copy(sysenv::StateEnvs)

Shallow copy of StateEnvs.

source
Base.lengthMethod
function Base.length(sysenv::StateEnvs)

Returns the length of the underlying MPS/Environment.

source
diff --git a/v0.1.0/mps/sweep/index.html b/v0.1.0/mps/sweep/index.html new file mode 100644 index 0000000..ad4786c --- /dev/null +++ b/v0.1.0/mps/sweep/index.html @@ -0,0 +1,11 @@ + +Sweeping through the MPS · TenNetLib.jl

Sweeping through the MPS

At a lower level of abstraction, TenNetLib.jl allows to control each fullsweep (left-to-right and right-to-left) manually to update StateEnvs.

Skip this part if you want to avoid lower-level abstraction.

SweepData

TenNetLib.jl defines a struct, called SweepData, to store essential data after each fullsweep.

TenNetLib.SweepDataType
mutable struct SweepData
+    sweepcount::Int
+    maxchi::Vector{Int}
+    energy::Vector{Float64}
+    entropy::Vector{Float64}
+    maxtruncerr::Vector{Float64}
+    lasteigs::Vector{Vector{Float64}}
+end

Holds historical data after each (full)sweep. Requires for convergence check etc.

  • sweepcount::Int: Number of fullsweeps performed.
  • maxchi::Vector{Int}: Maximum MPS bond/link dimensions after every sweep.
  • energy::Vector{Float64}: Energies after every sweep.
  • entropy::Vector{Float64}: Mid-chain entropies after every sweep.
  • maxtrucerr::Vector{Float64}: Maximum truncation error after every sweep.
  • lasteigs::Vector{Vector{Float64}}: Spectrum of eigenvalues at each bond after previous halfsweep.

Default constructor:

  • SweepData(): Initialize an empty SweepData object.
source
Base.copyMethod
Base.copy(swdata::SweepData)

Shallow copy of SweepData.

source

Perform a fullsweep

TenNetLib.fullsweep!Method
function fullsweep!(sysenv::StateEnvs, solver, nsite::Int, swdata::SweepData;
+                    kwargs...)

Perform a fullsweep (left-to-right and right-to-left) by solver.

Arguments:

  • sysenv::StateEnvs.
  • solver: Solver for update. Available ones: eig_solver and exp_solver.
  • nsite::Int of the environment. Either 1 or 2 for one-site or two-site update respectively.
  • swdata::SweepData.

Named arguments and their default values:

  • time_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for TDVP.
  • normalize::Bool = true: Whether to normalize after update.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • noise::Float64 = 0.0.
  • reverse_step::Bool = false if time_step = nothing, true otherwise.
  • outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true.
  • solver_tol::Float64 = 1E-14 if eig_solver, 1E-12 if exp_solver.
  • solver_krylovdim::Int = 5 if eig_solver, 30 if exp_solver.
  • solver_maxiter::Int = 2 if eig_solver, 100 if exp_solver.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false if eig_solver, true if exp_solver.
  • solver_check_convergence::Bool = false if eig_solver, true if exp_solver.

Return values:

  • ::Float64: Change in Energy ΔE
  • ::Float64: Change in Entropy ΔS

swdata::SweepData gets updated.

source

Perform a dynamical fullsweep

TenNetLib.jl defines the following function to dynamically decide whether to perform single- or two-site update at each bond, depending on the entropy growth at the previous halfsweep.

TenNetLib.dynamic_fullsweep!Method
function dynamic_fullsweep!(sysenv::StateEnvs, solver, swdata::SweepData;
+                            kwargs...)

Perform a dynamic fullsweep (left-to-right and right-to-left) by solver. The very first sweep, as dictated by swdata.sweepcount=0, Global Subspace Expansion (see below) is performed followed by a pure one-site sweep if typeof(sysenv) == StateEnvs{ProjMPO}, else performs a full two-site sweep. At each bond, if the lowest eigenvalue is below eigthreshold or the bond dimension at that bond has reached maxdim at a particular halfsweep, performs single-site update across that bond in the subsequent halfsweep, otherwise performs two-site update.

Arguments:

  • sysenv::StateEnvs.
  • solver: Solver for update. Available ones: eig_solver and exp_solver.
  • swdata::SweepData.

Named arguments and their default values:

  • time_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for TDVP.
  • normalize::Bool = true: Whether to normalize after update.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • noise::Float64 = 0.0.
  • reverse_step::Bool = false if time_step = nothing, true otherwise.
  • outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.
  • eigthreshold::Float64 = 1E-12.
  • extendat::Union{Nothing, Int} = nothing: If specified, at every extendatth sweep, Global Subspace Expansion is performed followed by a pure one-site sweep if typeof(sysenv) == StateEnvs{ProjMPO}, else performs a full two-site sweep.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true.
  • solver_tol::Float64 = 1E-14 if eig_solver, 1E-12 if exp_solver.
  • solver_krylovdim::Int = 3 if eig_solver, 30 if exp_solver.
  • solver_maxiter::Int = 1 if eig_solver, 100 if exp_solver.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false if eig_solver, true if exp_solver.
  • solver_check_convergence::Bool = false if eig_solver, true if exp_solver.

Arguments for Global Subspace Expansion and their default values:

  • extension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.
  • extension_applyH_cutoff::Float64 = 0.0: Cutoff for the application of the MPO to the MPS.
  • extension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension for the application of the MPO to the MPS.
  • extension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.

Return values:

  • ::Float64: Change in Energy ΔE
  • ::Float64: Change in Entropy ΔS

swdata::SweepData gets updated.

source

Global Subspace Expansion

Following Phys. Rev. B 102, 094315 (2020), a Global Subspace Expansion can be performed using Krylov subspace if the environments are created by a single MPO.

TenNetLib.krylov_extend!Method
function krylov_extend!(psi::MPS, H::MPO; kwargs...)

Performs Global Subspace Expansion.

Arguments and their default values:

  • extension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.
  • extension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.
  • extension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.
  • extension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.
source
TenNetLib.krylov_extend!Method
function krylov_extend!(sysenv::StateEnvs{ProjMPO}; kwargs...)

Performs Global Subspace Expansion. The StateEnvs must be created by a single MPO.

Arguments and their default values:

  • extension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.
  • extension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.
  • extension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.
  • extension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.
source
Info

Apart from TDVP, Global Subspace Expansion is also very useful for DMRG to get rid of nasty local minimas.

diff --git a/v0.1.0/mps/tdvp/index.html b/v0.1.0/mps/tdvp/index.html new file mode 100644 index 0000000..b7b2b4a --- /dev/null +++ b/v0.1.0/mps/tdvp/index.html @@ -0,0 +1,14 @@ + +Performing TDVP · TenNetLib.jl

Performing TDVP

TDVPEngine

TenNetLib.jl defines a struct, called TDVPEngine, to store essential data during TDVP sweeps.

TenNetLib.TDVPEngineType
mutable struct TDVPEngine{T <: Union{ProjMPO,
+                                     ProjMPOSum2,
+                                     ProjMPO_MPS2,
+                                     ProjMPOSum_MPS,
+                                     ProjCouplingModel,
+                                     ProjCouplingModel_MPS}}

Holds the MPS state, SweepData, and absolute elpased time for TDVP simulations.

  • sysenv::StateEnvs: Holds the state psi and environments PH.
  • swdata::SweepData: Holds the historical data after each (full)sweep.
  • abstime::Float64: Absolute elapsed time.
source
TenNetLib.TDVPEngineMethod
function TDVPEngine(psi::MPS, H::{T}) where T <: Union{MPO, Vector{MPO}, CouplingModel}

Constructor of the TDVPEngine from different forms of Hamiltonians.

source
TenNetLib.TDVPEngineMethod
function TDVPEngine(psi::MPS, H::T, Ms::Vector{MPS};
+                    weight::Float64) where T <: Union{MPO, Vector{MPO}, CouplingModel}

Constructor of TDVPEngine from different forms of Hamiltonians and a vector of MPS.

source
TenNetLib.maxchiMethod
function maxchi(engine::TDVPEngine)

Returns the maximum bond/link dimension of the state psi.

source
TenNetLib.totalerrorMethod
function totalerror(engine::TDVPEngine)

Returns the sum of the truncation errors of all the sweeps performed.

source
TenNetLib.krylov_extend!Method
function krylov_extend!(engine::TDVPEngine{ProjMPO}; kwargs...)

Performs Global Subspace Expansion.

Arguments and their default values:

  • extension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.
  • extension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.
  • extension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.
  • extension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.
source
TenNetLib.updateH!Method
function updateH!(engine::TDVPEngine, H::T;
+                  recalcEnv::Bool = true) where T <: Union{MPO, Vector{MPO}, CouplingModel}

Update Hamiltonian H in engine::TDVPEngine. If recalcEnv = false, it reuses previous environments. recalcEnv = false is only defined when the TDVPEngine is created from a single MPO.

source
TenNetLib.updateH!Method
function updateH!(engine::TDVPEngine, H::T, Ms::Vector{MPS};
+                  weight::Float64,
+                  recalcEnv::Bool = true) where T <: Union{MPO, Vector{MPO}, CouplingModel}

Update Hamiltonian H in engine::TDVPEngine. recalcEnv = false is not supported.

source
Base.copyMethod
Base.copy(engine::TDVPEngine)

Shallow copy of TDVPEngine.

source

tdvpsweep!

Following function performs one TDVP sweep.

TenNetLib.tdvpsweep!Function
tdvpsweep!(engine::TDVPEngine, time_step::Union{Float64, ComplexF64}; 
+           nsite::Union{Int, String} = "dynamic", 
+           solver = exp_solver,
+           kwargs...)::Nothing

Performs one TDVP sweep. Computes ψ' = exp(time_step * H) * ψ. Therefore, for real-time dynamics with step dt, time_step should be -im * dt.

Arguments:

  • engine::TDVPEngine.
  • time_step::Union{Float64, ComplexF64}.
  • nsite::Union{Int, String} = "dynamic": For two or one site sweeps, nsite=2 or nsite=1 respectively. For nsite="dynamic", dynamic_fullsweep! is performed.
  • solver = exp_solver: Only exp_solver is supported now.

Named arguments and their default values:

  • normalize::Bool = true: Whether to normalize after update.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.
  • eigthreshold::Float64 = 1E-12. Only applicable for nsite = "dynamic" (see dynamic_fullsweep!).
  • extendat::Union{Nothing, Int} = nothing: If specified, at every extendatth sweep, Global Subspace Expansion is performed followed by a pure one-site sweep if typeof(sysenv) == StateEnvs{ProjMPO}, else performs a full two-site sweep. Only applicable for nsite = "dynamic" (see dynamic_fullsweep!).

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true.
  • solver_tol::Float64 = 1E-12.
  • solver_krylovdim::Int = 30.
  • solver_maxiter::Int = 100.
  • solver_outputlevel::Int = 0.: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = true.
  • solver_check_convergence::Bool = true.

Arguments for Global Subspace Expansion and their default values:

Only applicable for nsite = "dynamic" (see dynamic_fullsweep!).

  • extension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.
  • extension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.
  • extension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.
  • extension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.
source
diff --git a/v0.1.0/mps/update_site/index.html b/v0.1.0/mps/update_site/index.html new file mode 100644 index 0000000..b64b44d --- /dev/null +++ b/v0.1.0/mps/update_site/index.html @@ -0,0 +1,2 @@ + +Perform local updates · TenNetLib.jl

Perform local updates

At the lowest-level of abstraction, TenNetLib.jl allows for updating the StateEnvs for each sites/bonds manually.

Skip this part if you want to avoid lower-level abstraction.

TenNetLib.update_position!Method
update_position!(sysenv::StateEnvs, solver, pos::Int, nsite::Int, ortho::String; kwargs...)

Updates StateEnvs at position pos by solver.

Arguments:

  • sysenv::StateEnvs
  • solver: Solver for update. Available ones: eig_solver and exp_solver.
  • pos::Int: Position of the bond (nsite=2) or site (nsite=1).
  • nsite of the environment. Either 1 or 2 for one-site or two-site update respectively.
  • ortho::String: Direction of the sweep. Either "left" or "right".

Named arguments and their default values:

  • time_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for TDVP.
  • normalize::Bool = true: Whether to normalize after update.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • noise::Float64 = 0.0.
  • reverse_step::Bool = false if time_step = nothing, true otherwise.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true.
  • solver_tol::Float64 = 1E-14 if eig_solver, 1E-12 if exp_solver.
  • solver_krylovdim::Int = 5 if eig_solver, 30 if exp_solver.
  • solver_maxiter::Int = 2 if eig_solver, 100 if exp_solver.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false if eig_solver, true if exp_solver.
  • solver_check_convergence::Bool = false if eig_solver, true if exp_solver.

Return values:

  • ::Float64: Energy.
  • ::Float64: Truncation Error.
  • ::Vector{Float64}: SVD spectrum.
source
diff --git a/v0.1.0/search_index.js b/v0.1.0/search_index.js new file mode 100644 index 0000000..30b926c --- /dev/null +++ b/v0.1.0/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"ttn/example_optimize/#Example:-Optimizing-TTN","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"","category":"section"},{"location":"ttn/example_optimize/#Ground-state-search","page":"Example: Optimizing TTN","title":"Ground state search","text":"","category":"section"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"A straight-forward TTN optimization can be performed as follows.","category":"page"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"using ITensors\nusing TenNetLib\n\nlet\n N = 32\n sites = siteinds(\"S=1/2\",N)\n os = OpStrings()\n \n for j=1:N-1\n os += 1, \"Sz\" => j, \"Sz\" => j+1\n os += 0.5, \"S+\" => j, \"S-\" => j+1\n os += 0.5, \"S-\" => j, \"S+\" => j+1\n end\n \n H = CouplingModel(os,sites)\n\n psi0 = default_randomTTN(sites, 12, QN(\"Sz\", 0))\n sweeppath = default_sweeppath(psi0)\n\n params = OptimizeParamsTTN(; nsweeps = [10, 10], maxdim = [20, 50],\n cutoff = 1e-14, noise = 1e-3, noisedecay = 2,\n disable_noise_after = 5)\n\n en, psi = optimize(psi0, H, params, sweeppath)\nend","category":"page"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"warning: Warning\nFor TTN optimzaion, direct MPO input is not supported. One can, however, prepare a CouplingModel from MPO using CouplingModel(mpos::MPO...). ","category":"page"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"Instead of using such higher-level code, one can also use lower-level functions for a better control.","category":"page"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"sysenv = StateEnvsTTN(psi0, H)\n\nswdata = optimize!(sysenv, params, sweeppath)\n\n# Get energy from `Sweepdata`\nenergy = swdata.energy[end]\n\n# take a shallow copy of the TTN\n# if the `StateEnvsTTN` will be updated later again\npsi = getpsi(sysenv)\n\n# Alternatively, take the psi from `StateEnvsTTN` itself.\n# NOTE: This can crash the simulation, if the TTN is modified (e.g., in measurements)\n# and `StateEnvsTTN` is going to be updated later on.\n# psi = sysenv.psi","category":"page"},{"location":"ttn/example_optimize/#Excited-state-search","page":"Example: Optimizing TTN","title":"Excited state search","text":"","category":"section"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"Excited state search is also straightforword.","category":"page"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"# Given a ground state `psi_gr`, initial TTN `psi0`,\n# and a Hamiltonian `H`\n\nen, psi = optimize(psi0, H, [psi_gr], params, sweeppath; weight = 10.0)","category":"page"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"Similarly, using StateEnvsTTN:","category":"page"},{"location":"ttn/example_optimize/","page":"Example: Optimizing TTN","title":"Example: Optimizing TTN","text":"sysenv_ex = StateEnvsTTN(psi0, H, [psi_gr]; weight = 10.0)\nswdata_ex = optimize!(sysenv_ex, params, sweeppath)\n\n# Get energy from `Sweepdata`\nenergy1 = swdata_ex.energy[end]\n\n# take a shallow copy of the TTN\n# if the `StateEnvsTTN` will be updated later again\npsi1 = getpsi(sysenv_ex)\n\n# Alternatively, take the psi from `StateEnvsTTN` itself.\n# NOTE: This can crash the simulation, if the TTN is modified (e.g., in measurements)\n# and `StateEnvsTTN` is going to be updated later.\n# psi1 = sysenv_ex.psi","category":"page"},{"location":"base/misc/#Miscellaneous-typedefs-and-functions","page":"Miscellaneous typedefs and functions","title":"Miscellaneous typedefs and functions","text":"","category":"section"},{"location":"base/misc/","page":"Miscellaneous typedefs and functions","title":"Miscellaneous typedefs and functions","text":"Vector2\nIDType\nIDTensors\ngen_rand_id\ncombineinds(inds::Vector{Index{Int}}; maxdim::Union{Nothing, Int} = nothing, kwargs...)\nindexintersection(inds1::Vector{Index{Int}}, inds2::Vector{Index{Int}}; maxdim::Union{Nothing, Int} = nothing, kwargs...)","category":"page"},{"location":"base/misc/#TenNetLib.Vector2","page":"Miscellaneous typedefs and functions","title":"TenNetLib.Vector2","text":"const Vector2{T} = Vector{Vector{T}}\n\nVector of Vectors.\n\n\n\n\n\n","category":"type"},{"location":"base/misc/#TenNetLib.IDType","page":"Miscellaneous typedefs and functions","title":"TenNetLib.IDType","text":"const IDType = ITensors.IDType\n\nType of randomly generated id. It is usually UInt64.\n\n\n\n\n\n","category":"type"},{"location":"base/misc/#TenNetLib.IDTensors","page":"Miscellaneous typedefs and functions","title":"TenNetLib.IDTensors","text":"const IDTensors = Dict{IDType, ITensor}\n\nDictionary of key = randomly generated id and value = ITensor objects.\n\n\n\n\n\n","category":"type"},{"location":"base/misc/#TenNetLib.gen_rand_id","page":"Miscellaneous typedefs and functions","title":"TenNetLib.gen_rand_id","text":"function gen_rand_id()\n\nGenerates a random id.\n\n\n\n\n\n","category":"function"},{"location":"base/misc/#TenNetLib.combineinds-Tuple{Vector{Index{Int64}}}","page":"Miscellaneous typedefs and functions","title":"TenNetLib.combineinds","text":"function combineinds(inds::Vector{Index};\n maxdim::Union{Nothing, Int} = nothing, \n maxqnblocks::Union{Nothing, Int} = nothing,\n kwargs...)\n\nCombine a vector of Index into one (like ITensors.jl's combiner). maxdim is be the maximum dimension of the output Index, maxqnblocks represents maximum number of QN blocks to retain in the output Index.\n\n\n\n\n\n","category":"method"},{"location":"base/misc/#TenNetLib.indexintersection-Tuple{Vector{Index{Int64}}, Vector{Index{Int64}}}","page":"Miscellaneous typedefs and functions","title":"TenNetLib.indexintersection","text":"function indexintersection(inds1::Vector{Index}, inds2::Vector{Index};\n maxdim::Union{Nothing, Int} = nothing,\n maxqnblocks::Union{Nothing, Int} = nothing,\n kwargs...)\n\nPerforms set intersection of two vectors of Index. maxdim is be the maximum dimension of the output Index, maxqnblocks represents maximum number of QN blocks to retain in the output Index.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#StateEnvs:-A-container-to-store-the-MPS-and-its-environments","page":"StateEnvs","title":"StateEnvs: A container to store the MPS and its environments","text":"","category":"section"},{"location":"mps/state_envs/","page":"StateEnvs","title":"StateEnvs","text":"At the lowest-level of abstraction, TenNetLib.jl defines StateEnvs to hold an MPS and its environments to be modified in place.","category":"page"},{"location":"mps/state_envs/","page":"StateEnvs","title":"StateEnvs","text":"Skip this part if you want to avoid lower-level abstraction.","category":"page"},{"location":"mps/state_envs/","page":"StateEnvs","title":"StateEnvs","text":"StateEnvs\ngetpsi(sysenv::StateEnvs)\ngetenv(sysenv::StateEnvs)\nStateEnvs(psi::MPS, H::MPO)\nStateEnvs(psi::MPS, Hs::Vector{MPO})\nStateEnvs(psi::MPS, H::MPO, Ms::Vector{MPS}; weight::Float64)\nStateEnvs(psi::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}; weight::Float64)\nStateEnvs(psi::MPS, H::CouplingModel)\nStateEnvs(psi::MPS, H::CouplingModel, Ms::Vector{MPS}; weight::Float64)\nupdateH!(sysenv::StateEnvs{ProjMPO}, H::MPO; recalcEnv::Bool = true)\nupdateH!(sysenv::StateEnvs{ProjMPOSum2}, Hs::Vector{MPO}; recalcEnv::Bool = true)\nupdateH!(sysenv::StateEnvs{ProjMPO_MPS2}, H::MPO, Ms::Vector{MPS}; weight::Float64, recalcEnv::Bool = true)\nupdateH!(sysenv::StateEnvs{ProjMPOSum_MPS}, H::Vector{MPO}, Ms::Vector{MPS}; weight::Float64, recalcEnv::Bool = true)\nupdateH!(sysenv::StateEnvs{ProjCouplingModel_MPS}, H::CouplingModel, Ms::Vector{MPS}; weight::Float64, recalcEnv::Bool = true)\nnsite(sysenv::StateEnvs)\nset_nsite!(sysenv::StateEnvs, nsite::Int)\nposition!(sysenv::StateEnvs, pos::Int)\nTenNetLib.product(sysenv::StateEnvs, v::ITensor)\nBase.copy(sysenv::StateEnvs)\nBase.length(sysenv::StateEnvs)","category":"page"},{"location":"mps/state_envs/#TenNetLib.StateEnvs","page":"StateEnvs","title":"TenNetLib.StateEnvs","text":"mutable struct StateEnvs{T <: Union{ProjMPO,\n ProjMPO_MPS2,\n ProjMPOSum2,\n ProjMPOSum_MPS,\n ProjCouplingModel,\n ProjCouplingModel_MPS}\n }\n psi::MPS\n PH::T\nend\n\nHolds the MPS state psi and its environments PH.\n\n\n\n\n\n","category":"type"},{"location":"mps/state_envs/#TenNetLib.getpsi-Tuple{StateEnvs}","page":"StateEnvs","title":"TenNetLib.getpsi","text":"function getpsi(sysenv::StateEnvs)\n\nReturns (shallow copy of) the state psi.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.getenv-Tuple{StateEnvs}","page":"StateEnvs","title":"TenNetLib.getenv","text":"function getenv(sysenv::StateEnvs)\n\nReturns (shallow copy of) the environment PH.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.StateEnvs-Tuple{MPS, MPO}","page":"StateEnvs","title":"TenNetLib.StateEnvs","text":"function StateEnvs(psi::MPS, H::MPO)\n\nConstructor of the StateEnvs from a single MPO.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.StateEnvs-Tuple{MPS, Vector{MPO}}","page":"StateEnvs","title":"TenNetLib.StateEnvs","text":"function StateEnvs(psi::MPS, Hs::Vector{MPO})\n\nConstructor of the StateEnvs from a vector of MPO. Environments are contracted in parallel.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.StateEnvs-Tuple{MPS, MPO, Vector{MPS}}","page":"StateEnvs","title":"TenNetLib.StateEnvs","text":"function StateEnvs(psi::MPS, H::MPO, Ms::Vector{MPS}; weight::Float64)\n\nConstructor of the StateEnvs from a single MPO and a vector of MPS used for excited state DMRG.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.StateEnvs-Tuple{MPS, Vector{MPO}, Vector{MPS}}","page":"StateEnvs","title":"TenNetLib.StateEnvs","text":"function StateEnvs(psi::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}; weight::Float64)\n\nConstructor of the StateEnvs from a vector of MPO and a vector of MPS used for excited state DMRG. Environments for MPOs are contracted in parallel.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.StateEnvs-Tuple{MPS, CouplingModel}","page":"StateEnvs","title":"TenNetLib.StateEnvs","text":"function StateEnvs(psi::MPS, H::CouplingModel)\n\nConstructor of the StateEnvs from a CouplingModel. Each terms in the CouplingModel are contracted in parallel.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.StateEnvs-Tuple{MPS, CouplingModel, Vector{MPS}}","page":"StateEnvs","title":"TenNetLib.StateEnvs","text":"function StateEnvs(psi::MPS, H::CouplingModel, Ms::Vector{MPS}; weight::Float64)\n\nConstructor of StateEnvs from a CouplingModel and a vector of MPS used for excited state DMRG. Each terms in the CouplingModel are contracted in parallel.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.updateH!-Tuple{StateEnvs{ProjMPO}, MPO}","page":"StateEnvs","title":"TenNetLib.updateH!","text":"function updateH!(sysenv::StateEnvs{ProjMPO}, H::MPO; recalcEnv::Bool = true)\n\nUpdate Hamiltonian H in sysenv::StateEnvs. If recalcEnv = false, it reuses previous environments.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.updateH!-Tuple{StateEnvs{ProjMPOSum2}, Vector{MPO}}","page":"StateEnvs","title":"TenNetLib.updateH!","text":"function updateH!(sysenv::StateEnvs{ProjMPOSum2}, Hs::Vector{MPO}; recalcEnv::Bool = true)\n\nUpdate Hamiltonian H in sysenv::StateEnvs. recalcEnv = false is not supported.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.updateH!-Tuple{StateEnvs{ProjMPO_MPS2}, MPO, Vector{MPS}}","page":"StateEnvs","title":"TenNetLib.updateH!","text":"function updateH!(sysenv::StateEnvs{ProjMPO_MPS2}, H::MPO, Ms::Vector{MPS};\n weight::Float64, recalcEnv::Bool = true)\n\nUpdate Hamiltonian H in sysenv::StateEnvs. recalcEnv = false is not supported.\n\nweight::Union{Nothing, Float64} = nothing.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.updateH!-Tuple{StateEnvs{ProjMPOSum_MPS}, Vector{MPO}, Vector{MPS}}","page":"StateEnvs","title":"TenNetLib.updateH!","text":"function updateH!(sysenv::StateEnvs{ProjMPOSum_MPS}, Hs::Vector{MPO}, Ms::Vector{MPS};\n weight::Float64, recalcEnv::Bool = true)\n\nUpdate Hamiltonian H in sysenv::StateEnvs. recalcEnv = false is not supported.\n\nweight::Union{Nothing, Float64} = nothing.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.updateH!-Tuple{StateEnvs{ProjCouplingModel_MPS}, CouplingModel, Vector{MPS}}","page":"StateEnvs","title":"TenNetLib.updateH!","text":"function updateH!(sysenv::StateEnvs{ProjCouplingModel_MPS}, H::CouplingModel, Ms::Vector{MPS};\n weight::Float64, recalcEnv::Bool = true)\n\nUpdate Hamiltonian H in sysenv::StateEnvs. recalcEnv = false is not supported.\n\nweight::Union{Nothing, Float64} = nothing.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#ITensors.nsite-Tuple{StateEnvs}","page":"StateEnvs","title":"ITensors.nsite","text":"function nsite(sysenv::StateEnvs)\n\nReturns the nsite of the environment. nsite = 1 for single-site environment, nsite = 2 for two-site environmrnt, and so on. Currently, only uses nsite = 0, 1, or 2.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#ITensors.set_nsite!-Tuple{StateEnvs, Int64}","page":"StateEnvs","title":"ITensors.set_nsite!","text":"function set_nsite!(sysenv::StateEnvs, nsite::Int)\n\nSet nsite of the environment. nsite = 1 for single-site environment, nsite = 2 for two-site environmrnt, and so on. Currently, only uses nsite = 0, 1, or 2.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#ITensors.position!-Tuple{StateEnvs, Int64}","page":"StateEnvs","title":"ITensors.position!","text":"function position!(sysenv::StateEnvs, pos::Int)\n\nCompute the left and right environments at position pos.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#TenNetLib.product-Tuple{StateEnvs, ITensor}","page":"StateEnvs","title":"TenNetLib.product","text":"function product(sysenv::StateEnvs, v::ITensor)\n\nReturns the Matrix-Vector product between the environment and input ITensor v.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#Base.copy-Tuple{StateEnvs}","page":"StateEnvs","title":"Base.copy","text":"function Base.copy(sysenv::StateEnvs)\n\nShallow copy of StateEnvs.\n\n\n\n\n\n","category":"method"},{"location":"mps/state_envs/#Base.length-Tuple{StateEnvs}","page":"StateEnvs","title":"Base.length","text":"function Base.length(sysenv::StateEnvs)\n\nReturns the length of the underlying MPS/Environment.\n\n\n\n\n\n","category":"method"},{"location":"mps/dmrg/#Performing-DMRG","page":"Performing DMRG","title":"Performing DMRG","text":"","category":"section"},{"location":"mps/dmrg/","page":"Performing DMRG","title":"Performing DMRG","text":"Functions to perfom (and control) DMRG runs.","category":"page"},{"location":"mps/dmrg/#DMRGParams","page":"Performing DMRG","title":"DMRGParams","text":"","category":"section"},{"location":"mps/dmrg/","page":"Performing DMRG","title":"Performing DMRG","text":"TenNetLib.jl defines a struct, called DMRGParams, to control DMRG simulations.","category":"page"},{"location":"mps/dmrg/","page":"Performing DMRG","title":"Performing DMRG","text":"DMRGParams\nDMRGParams(;maxdim::Vector{Int}, nsweeps::Vector{Int}, cutoff::Union{Vector{Float64}, Float64} = _Float64_Threshold, noise::Union{Vector{Float64}, Float64, Int} = 0.0, noisedecay::Union{Vector{Float64}, Float64, Int} = 1.0, disable_noise_after::Union{Vector{Int}, Int} = typemax(Int))\nBase.copy(params::DMRGParams)","category":"page"},{"location":"mps/dmrg/#TenNetLib.DMRGParams","page":"Performing DMRG","title":"TenNetLib.DMRGParams","text":"mutable struct DMRGParams\n maxdim::Vector{Int}\n nsweeps::Vector{Int}\n cutoff::Vector{Float64}\n noise::Vector{Float64}\n noisedecay::Vector{Float64}\n disable_noise_after::Vector{Int}\nend\n\nHolds parameters to control DMRG sweeps.\n\nmaxdim::Vector{Int}: Maximum allowed MPS bond/link dimensions at each stages of DMRG.\nnsweeps::Vector{Int}: Number of sweeps to be performed at each statges of DMRG.\ncutoff::Vector{Float64}: Cutoff for SVD truncation at each stages of DMRG.\nnoise::Vector{Float64}: Noise level at each stages of DMRG.\nnoisedecay::Vector{Float64}: Decay of noise level at each states of DMRG. Noise is divided by noisedecay after each sweep.\ndisable_noise_after::Vector{Int}: Switch of noise after this many sweeps at each\n\nstates of DMRG.\n\nAll these Vectors must have same dimension.\n\n\n\n\n\n","category":"type"},{"location":"mps/dmrg/#TenNetLib.DMRGParams-Tuple{}","page":"Performing DMRG","title":"TenNetLib.DMRGParams","text":"function DMRGParams(;maxdim::Vector{Int}, nsweeps::Vector{Int}, \n cutoff::Union{Vector{Float64}, Float64} = _Float64_Threshold,\n noise::Union{Vector{Float64}, Float64, Int} = 0.0,\n noisedecay::Union{Vector{Float64}, Float64, Int} = 1.0,\n disable_noise_after::Union{Vector{Int}, Int} = typemax(Int))\n\nConstructor for DMRGParams. Takes only named arguments.\n\nmaxdim::Vector{Int}: Maximum allowed MPS bond/link dimensions at each stages of DMRG.\nnsweeps::Vector{Int}: Number of sweeps to be performed at each statges of DMRG.\ncutoff::Union{Float64, Vector{Float64}} = Float64_threshold(): Cutoff for SVD truncation at each stages of DMRG. If Float64, cutoff remains same throughout the DMRG simulation. \nnoise::Union{Float64, Int, Vector{Float64}} = 0.0: Noise level at each stages of DMRG. If Float64 or Int, initial noise remains same throughout the DMRG simulation.\nnoisedecay::Union{Float64, Int, Vector{Float64}} = 1.0: Decay of noise level at each states of DMRG. Noise is divided by noisedecay after each sweep. If Float64 or Int, noisedecay remains same throughout the DMRG simulation.\ndisable_noise_after::Union{Int, Vector{Int}} = typemax(Int): Switch of noise after this many sweeps at each states of DMRG. If Int, disable_noise_after remains same throughout the DMRG simulation.\n\n\n\n\n\n","category":"method"},{"location":"mps/dmrg/#Base.copy-Tuple{DMRGParams}","page":"Performing DMRG","title":"Base.copy","text":"Base.copy(params::DMRGParams)\n\nShallow copy DMRGParams.\n\n\n\n\n\n","category":"method"},{"location":"mps/dmrg/#A-lower-level-DMRG-function","page":"Performing DMRG","title":"A lower level DMRG function","text":"","category":"section"},{"location":"mps/dmrg/","page":"Performing DMRG","title":"Performing DMRG","text":"Following function modifies StateEnvs in-place. Skip this function if you want to avoid lower-level abstraction.","category":"page"},{"location":"mps/dmrg/","page":"Performing DMRG","title":"Performing DMRG","text":"dmrg!(sysenv::StateEnvs, params::DMRGParams, nsite::Int; kwargs...)","category":"page"},{"location":"mps/dmrg/#TenNetLib.dmrg!-Tuple{StateEnvs, DMRGParams, Int64}","page":"Performing DMRG","title":"TenNetLib.dmrg!","text":"function dmrg!(sysenv::StateEnvs, params::DMRGParams, nsite::Int; kwargs...)\n\nPerforms DMRG.\n\nArguments:\n\nsysenv::StateEnvs.\nparams::DMRGParams.\nnsite::Int of the environment. Either 1 or 2 for one-site or two-site update respectively.\n\nNamed arguments and their default values:\n\nnormalize::Bool = true: Whether to normalize after update.\nsvd_alg::String = \"divide_and_conquer\".\nweight::Float64 = -1.0: Weight for the excited state DMRG. Must be set to greater than 0 for the excited state DMRG.\noutputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.\n\nConvergence criteria:\n\nenergyErrGoal: DMRG (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.\nentropyErrGoal: DMRG (at a particluar stage) stops when mid-chain entropy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.\n\nWhen both energyErrGoal and entropyErrGoal are given, both conditions must be satisfied to trigger this early stopping.\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true.\nsolver_tol::Float64 = 1E-14.\nsolver_krylovdim::Int = 5.\nsolver_maxiter::Int = 2.\nsolver_outputlevel::Int = 0.: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false.\nsolver_check_convergence::Bool = false.\n\nReturn values:\n\nSweepData\n\n\n\n\n\n","category":"method"},{"location":"mps/dmrg/#Higher-level-DMRG-functions","page":"Performing DMRG","title":"Higher level DMRG functions","text":"","category":"section"},{"location":"mps/dmrg/","page":"Performing DMRG","title":"Performing DMRG","text":"Standard two- and single-site DMRG functions. Single-site DMRG can increasing the bond-dimension if noise > Float64_threshold().","category":"page"},{"location":"mps/dmrg/","page":"Performing DMRG","title":"Performing DMRG","text":"dmrg2(psi0::MPS, H::T, params::DMRGParams; kwargs...) where T <: Union{MPO, Vector{MPO}, CouplingModel}\ndmrg1(psi0::MPS, H::T, params::DMRGParams; kwargs...) where T <: Union{MPO, Vector{MPO}, CouplingModel}","category":"page"},{"location":"mps/dmrg/#TenNetLib.dmrg2-Union{Tuple{T}, Tuple{MPS, T, DMRGParams}} where T<:Union{MPO, CouplingModel, Vector{MPO}}","page":"Performing DMRG","title":"TenNetLib.dmrg2","text":"function dmrg2(psi0::MPS, H::MPO, params::DMRGParams; kwargs...)\nfunction dmrg2(psi0::MPS, H::CouplingModel, params::DMRGParams; kwargs...)\nfunction dmrg2(psi0::MPS, Hs::Vector{MPO}, params::DMRGParams; kwargs...)\nfunction dmrg2(psi0::MPS, H::MPO, Ms::Vector{MPS}, params::DMRGParams; kwargs...)\nfunction dmrg2(psi0::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}, params::DMRGParams; kwargs...)\nfunction dmrg2(psi0::MPS, H::CouplingModel, Ms::Vector{MPS}, params::DMRGParams; kwargs...)\n\nPerforms two-site DMRG.\n\nArguments:\n\npsi0::MPS: Initial MPS.\nH::MPO, H::CouplingModel, Hs::Vector{MPO}, Ms::Vector{MPS}.\nparams::DMRGParams.\n\nNamed arguments and their default values:\n\nnormalize::Bool = true: Whether to normalize after update.\nsvd_alg::String = \"divide_and_conquer\".\nweight::Float64 = -1.0: Weight for the excited state DMRG. Must be set to greater than 0 for the excited state DMRG.\noutputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.\n\nConvergence criteria:\n\nenergyErrGoal: DMRG (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.\nentropyErrGoal: DMRG (at a particluar stage) stops when mid-chain entropy difference between two consecutive sweeps falls below this threshold and DMRG moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.\n\nWhen both energyErrGoal and entropyErrGoal are given, both conditions must be satisfied to trigger this early stopping.\n\nNamed arguments for eig_solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true.\nsolver_tol::Float64 = 1E-14.\nsolver_krylovdim::Int = 5.\nsolver_maxiter::Int = 2.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false.\nsolver_check_convergence::Bool = false.\n\nReturn values:\n\n::Float64: Energy.\n::MPS: The state psi.\n\n\n\n\n\n","category":"method"},{"location":"mps/dmrg/#TenNetLib.dmrg1-Union{Tuple{T}, Tuple{MPS, T, DMRGParams}} where T<:Union{MPO, CouplingModel, Vector{MPO}}","page":"Performing DMRG","title":"TenNetLib.dmrg1","text":"function dmrg1(psi0::MPS, H::MPO, params::DMRGParams; kwargs...)\nfunction dmrg1(psi0::MPS, H::CouplingModel, params::DMRGParams; kwargs...)\nfunction dmrg1(psi0::MPS, Hs::Vector{MPO}, params::DMRGParams; kwargs...)\nfunction dmrg1(psi0::MPS, H::MPO, Ms::Vector{MPS}, params::DMRGParams; kwargs...)\nfunction dmrg1(psi0::MPS, Hs::Vector{MPO}, Ms::Vector{MPS}, params::DMRGParams; kwargs...)\nfunction dmrg1(psi0::MPS, H::CouplingModel, Ms::Vector{MPS}, params::DMRGParams; kwargs...)\n\nPerforms single-site DMRG. All other details are same as in dmrg2.\n\n\n\n\n\n","category":"method"},{"location":"mps/example_tdvp/#Example:-TDVP","page":"Example: TDVP","title":"Example: TDVP","text":"","category":"section"},{"location":"mps/example_tdvp/#Time-evolution-with-time-dependent-variational-principle-(TDVP).","page":"Example: TDVP","title":"Time-evolution with time dependent variational principle (TDVP).","text":"","category":"section"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"A straight-forward TDVP (with dynamical sweeps) can be performed as follows. Note that TDVP computes ψ' = exp(time_step * H) * ψ. Therefore, for real-time dynamics with step dt, time_step should be -im * dt.","category":"page"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"using ITensors\nusing TenNetLib\n\nlet\n N = 32\n sites = siteinds(\"S=1/2\",N)\n os = OpSum()\n \n for j=1:N-1\n os += 1, \"Sz\", j, \"Sz\", j+1\n os += 0.5, \"S+\", j, \"S-\", j+1\n os += 0.5, \"S-\", j, \"S+\", j+1\n end\n \n H = MPO(os,sites)\n states = [isodd(n) ? \"Up\" : \"Dn\" for n in 1:N]\n psi0 = MPS(sites, states)\n\n tau = -0.01im \n engine = TDVPEngine(psi0, H)\n for ii = 1:100\n\n \t# `nsite = \"dynamic\"` for dynamical selection between\n\t# single- and two-site variants at different bonds\n tdvpsweep!(engine, tau,\n nsite = \"dynamic\";\n maxdim = 200,\n cutoff = 1E-12,\n extendat = 5)\n\n\t# Errors in the last sweep and the total error till this point\n\tswerr = sweeperror(engine)\n\ttotalerr = totalerror(engine)\n\t\n\tpsi = getpsi(engine)\n\t\n\t# DO STUFF\n end\nend","category":"page"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"Here, we have used OpSum and MPO. Alternatively, standard OpStrings and CouplingModel can be used.","category":"page"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"Optionally, one can use pure single- or two-site updates. If the TDVPEngine is created with a single MPO then Global Subspace Expansion can be performed.","category":"page"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"for ii = 1:100\n\n # GSE at every 5th sweep.\n if ii % 5 == 1\n krylov_extend!(engine)\n end\n \n # `nsite = 1` for single-site update\n tdvpsweep!(engine, tau,\n nsite = 1;\n maxdim = 200,\n cutoff = 1E-12)\n\n # Errors in the last sweep and the total error till this point\n swerr = sweeperror(engine)\n totalerr = totalerror(engine)\n\t\n psi = getpsi(engine)\n\t\n # DO STUFF\nend","category":"page"},{"location":"mps/example_tdvp/#Time-evolution-with-time-dependent-Hamiltonian","page":"Example: TDVP","title":"Time-evolution with time-dependent Hamiltonian","text":"","category":"section"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"For time-dependent Hamiltonian, updateH! can be used.","category":"page"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"using ITensors\nusing TenNetLib\n\nfunction makeHt(sites, t)\n\n os = OpSum() \n for j=1:N-1\n os += 1, \"Sz\", j, \"Sz\", j+1\n os += 0.5, \"S+\", j, \"S-\", j+1\n os += 0.5, \"S-\", j, \"S+\", j+1\n end\n for j=1:N\n os += t, \"Sz\", j\n end\n return MPO(os,sites)\nend\n\nlet\n N = 32\n sites = siteinds(\"S=1/2\",N)\n\n states = [isodd(n) ? \"Up\" : \"Dn\" for n in 1:N]\n psi0 = MPS(sites, states)\n\n dt = 0.01\n tau = -im * dt\n\n H0 = makeHt(sites, 0.0)\n engine = TDVPEngine(psi0, H0)\n \n for ii = 1:100\n\n \t# `nsite = \"dynamic\"` for dynamical selection between\n\t# single- and two-site variants at different bonds\n tdvpsweep!(engine, tau,\n nsite = \"dynamic\";\n maxdim = 200,\n cutoff = 1E-12,\n extendat = 5)\n\n\t# Errors in the last sweep and the total error till this point\n\tswerr = sweeperror(engine)\n\ttotalerr = totalerror(engine)\n\t\n\tpsi = getpsi(engine)\n\t\n\t# DO STUFF\n\n\t# update Hamiltonian for the next iteration\n\tHt = makeHt(sites, ii*dt)\n\tupdateH!(engine, Ht)\n end\nend","category":"page"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"Note 1: The above example for time-dependent Hamiltonian is very crude. In real situations, the update in the Hamiltonian should be done with proper care.","category":"page"},{"location":"mps/example_tdvp/","page":"Example: TDVP","title":"Example: TDVP","text":"Note 2: When the TDVPEngine is created from a single MPO and dt is small, one can use recalcEnv = false in updateH!, so that environments from the last step is reused.","category":"page"},{"location":"mps/measure/#Measuring-the-MPS","page":"Measuring the MPS","title":"Measuring the MPS","text":"","category":"section"},{"location":"mps/measure/","page":"Measuring the MPS","title":"Measuring the MPS","text":"TenNetLib.entropy(psi::MPS, bond::Int)\nTenNetLib.entropy(psi::MPS; kwargs...)\nmeasure(::Type{T}, psi::MPS, opten::ITensor) where T <: Union{ComplexF64, Float64}\nmeasure(::Type{T}, psi::MPS, opstr::String, pos::Int) where T <: Union{ComplexF64, Float64}\nmeasure(::Type{T}, psi::MPS, opstr::String; kwargs...) where T <: Union{ComplexF64, Float64}\nmeasure(::Type{T}, psi::MPS, optens::Vector{ITensor}) where T <: Union{ComplexF64, Float64}\nmeasure(::Type{T}, psi::MPS, oppairs::Vector{Pair{String, Int}}; isfermions::Bool = true) where T <: Union{ComplexF64, Float64}","category":"page"},{"location":"mps/measure/#TenNetLib.entropy-Tuple{MPS, Int64}","page":"Measuring the MPS","title":"TenNetLib.entropy","text":"function entropy(psi::MPS, bond::Int)\n\nCompute von Neumann Entropy of a given MPS psi at bond.\n\n\n\n\n\n","category":"method"},{"location":"mps/measure/#TenNetLib.entropy-Tuple{MPS}","page":"Measuring the MPS","title":"TenNetLib.entropy","text":"function entropy(psi::MPS; kwargs...)\n\nCompute von Neumann Entropies of a given MPS psi at all the bonds.\n\nOptionally, for specific bonds, keyword argument bonds can be specified, e.g., bonds = [1, 2, 3].\n\n\n\n\n\n","category":"method"},{"location":"mps/measure/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, MPS, ITensor}} where T<:Union{Float64, ComplexF64}","page":"Measuring the MPS","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::MPS, opten::ITensor)\n\nReturns (complex / real) local expectation value (::ComplexF64 / ::Float64) of a given MPS psi::MPS. The operator opten::ITensor must be single-site operator.\n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\n\n\n\n\n","category":"method"},{"location":"mps/measure/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, MPS, String, Int64}} where T<:Union{Float64, ComplexF64}","page":"Measuring the MPS","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::MPS, opstr::String, pos::Int)\n\nReturns (complex / real) local expectation value (::ComplexF64 / ::Float64) of a given MPS psi::MPS for a given operator name (opstr::String) and a site index (pos::Int) \n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\n\n\n\n\n","category":"method"},{"location":"mps/measure/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, MPS, String}} where T<:Union{Float64, ComplexF64}","page":"Measuring the MPS","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::MPS, opstr::String; kwargs...)\n\nReturns (complex / real) local expectation values (::Vector{ComplexF64} / ::Vector{Float64}) of a given MPS psi::MPS for a given operator name (opstr::String) at all the sites.\n\nOptionally, for specific sites, keyword argument sites can be specified, e.g., sites = [1, 2, 3].\n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\n\n\n\n\n","category":"method"},{"location":"mps/measure/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, MPS, Vector{ITensor}}} where T<:Union{Float64, ComplexF64}","page":"Measuring the MPS","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::MPS, optens::Vector{ITensor})\n\nReturns (complex / real) multi-site expectation value (::ComplexF64 / ::Float64) of a given MPS psi::MPS for a given vector of single-site operators (optens::Vector{ITensor}).\n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\n\n\n\n\n","category":"method"},{"location":"mps/measure/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, MPS, Vector{Pair{String, Int64}}}} where T<:Union{Float64, ComplexF64}","page":"Measuring the MPS","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::MPS, oppairs::Vector{Pair{String, Int}};\n isfermions::Bool = true)\n\nReturns (complex / real) multi-site expectation value (::ComplexF64 / ::Float64) of a given MPS psi::MPS. oppairs::Vector{Pair{String, Int}} contains pairs of operator names (String) and site locations (Int). E.g., for <ψ|OᵢOⱼOₖ... |ψ>, oppairs = [\"O\" => i, \"O\" => j, \"O\" => k,...].\n\nFermionic JW strings are added automatically for fermionic operators if isfermions::Bool = true (default).\n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\nExample:\n\nvalueC = measure(psi, [\"Cdag\" => 2, \"C\" => 6, \"Cdag\" => 9, \"C\" => 12])\nvalueR = measure(Float64, psi, [\"Cdag\" => 2, \"C\" => 6, \"Cdag\" => 9, \"C\" => 12])\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn/#Tree-Tensor-Networks-(TTN)","page":"Tree Tensor Networks","title":"Tree Tensor Networks (TTN)","text":"","category":"section"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"Tree Tensor Network (TTN) is a loop-free hierarchical tensor network (see belew).","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"Tree Tensor Network for a system of size 16\n(Image: Tree Tensor Network)","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"Due to enhanced connectivity in the structure of TTN, it can support long-range quantum correlations comapred to MPS. Moreover, simulations for systems with periodic boundary conditions (PBC) are almost as efficient as the same with open boundary conditions (OBC). TTNs have found their place for simulating 2D or pseudo-2D ladder/cylinder systems with PBC where the performance of MPS is not adequate.","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"TenNetLib.jl implements the unconstrained optimization for obtaining ground as well as excited states as described in Phys. Rev. B 90, 125154 (2014) and SciPost Phys. Lect. Notes 8 (2019).","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"Each tensor in the TTN are indexed by a pair (Tuple) of Ints = (ll, nn).","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"Int2","category":"page"},{"location":"ttn/ttn/#TenNetLib.Int2","page":"Tree Tensor Networks","title":"TenNetLib.Int2","text":"const Int2 = Tuple{Int, Int}\n\nTuple of two Ints. \n\n\n\n\n\n","category":"type"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"In the default scenario, ll denotes the layer index and nn denotes the tensor index at each layer (see the image above). The counting for ll, in the default case, starts at the bottom (towards to top level), while nn counts from left. The structure of the network is defined by a Graph{Int2} object. The link / bond between two neighboring nodes is denoted by a LinkTypeTTN object, an unordered pair of Int2s.","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"LinkTypeTTN","category":"page"},{"location":"ttn/ttn/#TenNetLib.LinkTypeTTN","page":"Tree Tensor Networks","title":"TenNetLib.LinkTypeTTN","text":"struct LinkTypeTTN\n first::Int2\n second::Int2\nend\n\nLink / bond between two nodes first and second.\n\n\n\n\n\n","category":"type"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"info: Info\nThe order of the nodes inside LinkTypeTTN is irrelevant, i.e., LinkTypeTTN(node1, node2) == LinkTypeTTN(node2, node1).","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"info: Info\nTenNetLib.jl can automatically handle system-sizes that are not powers of 2. No special care is needed for such system-sizes.","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"TTN for system-size 12 TTN for system-size 14\nSites 1, 4, 7, 11 are directly connected to ll=2 tensors Sites 5, 12 are directly connected to ll=2 tensors\nNodes (1,1), (1,3), (1,5), (1,7) are removed Nodes (1,3), (1,7) are removed\n(Image: TTN size 12) (Image: TTN size 14)","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"info: Info\nThe TTN codes defined in TenNetLib.jl can readily work, without any changes, for any loop-free tensor networks, e.g., Fork Tensor Networks.","category":"page"},{"location":"ttn/ttn/","page":"Tree Tensor Networks","title":"Tree Tensor Networks","text":"tip: Tip\nFor 2D systems, use a mapping from the 2D lattice to a 1D chain using Hilbert curve, as shown in Quantum 5, 556 (2021)","category":"page"},{"location":"base/graph/#The-Graph-object","page":"The Graph object","title":"The Graph object","text":"","category":"section"},{"location":"base/graph/","page":"The Graph object","title":"The Graph object","text":"TenNetLib.jl defines its own undirected graph object, the Graph. Currently only used for the Tree Tensor Network (TTN) codes.","category":"page"},{"location":"base/graph/","page":"The Graph object","title":"The Graph object","text":"Graph\nGraph{T}() where T\nGraph{T}(nodes::Set{T}) where T\ngetnodes(graph::Graph{T}) where T\nhasnode(graph::Graph{T}, node::T) where T\naddnode!(graph::Graph{T}, node::T) where T\naddedge!(graph::Graph{T}, node1::T, node2::T) where T\nisneighbor(graph::Graph{T}, node1::T, node2::T) where T\nbfs(graph::Graph{T}, source::T, destination::Union{Nothing, T} = nothing) where T\nnodes_from_bfs(graph::Graph{T}, source::T;reverse::Bool = false) where T\nshortest_path(graph::Graph{T}, source::T, destination::T) where T\nnextnode_in_path(graph::Graph{T}, source::T, destination::T, n=1) where T\nhas_cycle(graph::Graph{T}) where T\nfind_sum_central_node(graph::Graph{T}, nodes::Union{Nothing, Set{T}} = nothing) where T\nfind_eccentric_central_node(graph::Graph{T}, nodes::Union{Nothing, Set{T}} = nothing) where T\nBase.copy(graph::Graph{T}) where T\nBase.getindex(graph::Graph{T}, node::T) where T\nBase.setindex!(graph::Graph{T}, neighbors::Set{T}, node::T) where T\nBase.:(==)(graph1::Graph{T}, graph2::Graph{T}) where T","category":"page"},{"location":"base/graph/#TenNetLib.Graph","page":"The Graph object","title":"TenNetLib.Graph","text":"mutable struct Graph{T}\n nodes::Set{T}\n edges::Dict{T, Set{T}}\nend\n\nUndirected graph where nodes are of type T.\n\nnodes::Set{T}: Holds the nodes of the graph.\nedges::Dict{T, Set{T}}: Holds the edges of the graph. For a given node as key, holds all the connected nodes as value of the Dict.\n\n\n\n\n\n","category":"type"},{"location":"base/graph/#TenNetLib.Graph-Union{Tuple{}, Tuple{T}} where T","page":"The Graph object","title":"TenNetLib.Graph","text":"function Graph{T}()\n\nContructor of empty Graph.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.Graph-Union{Tuple{Set{T}}, Tuple{T}} where T","page":"The Graph object","title":"TenNetLib.Graph","text":"function Graph{T}(nodes::Set{T}) where T\nfunction Graph{T}(nodes::Vector{T}) where T\n\nConstructor of Graph with a list of nodes and empty edges.\n\nnodes: Intial nodes.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.getnodes-Union{Tuple{Graph{T}}, Tuple{T}} where T","page":"The Graph object","title":"TenNetLib.getnodes","text":"function getnodes(graph::Graph{T}) where T = copy(graph.nodes)\n\nReturns (shallow copy of) nodes in the Graph.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.hasnode-Union{Tuple{T}, Tuple{Graph{T}, T}} where T","page":"The Graph object","title":"TenNetLib.hasnode","text":"function hasnode(graph::Graph{T}, node::T) where T\n\nChecks whether a node is in the Graph.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.addnode!-Union{Tuple{T}, Tuple{Graph{T}, T}} where T","page":"The Graph object","title":"TenNetLib.addnode!","text":"function addnode!(graph::Graph{T}, node::T) where T\n\nAdds a node to the Graph.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.addedge!-Union{Tuple{T}, Tuple{Graph{T}, T, T}} where T","page":"The Graph object","title":"TenNetLib.addedge!","text":"function addedge!(graph::Graph{T}, node1::T, node2::T) where T\n\nAdds an edge between node1 and node2. If node1 or node2 are not present in the Graph, they are added.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.isneighbor-Union{Tuple{T}, Tuple{Graph{T}, T, T}} where T","page":"The Graph object","title":"TenNetLib.isneighbor","text":"function isneighbor(graph::Graph{T}, node1::T, node2::T)::Bool where T\n\nChecks whether node1 and node2 are connected by an edge.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.bfs-Union{Tuple{T}, Tuple{Graph{T}, T}, Tuple{Graph{T}, T, Union{Nothing, T}}} where T","page":"The Graph object","title":"TenNetLib.bfs","text":"function bfs(graph::Graph{T},\n source::T,\n destination::Union{Nothing, T} = nothing) where T\n\nPerforms a full BFS starting from the node source (and optionally, to the destination).\n\nReturn values\n\n::Dict{T, Int}: Distances of nodes (key) in the BFS path.\n::Dict{T, T}: Parents of nodes (key) in the BFS path.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.nodes_from_bfs-Union{Tuple{T}, Tuple{Graph{T}, T}} where T","page":"The Graph object","title":"TenNetLib.nodes_from_bfs","text":"function nodes_from_bfs(graph::Graph{T}, source::T;\n reverse::Bool = false) where T\n\nfunction nodes_from_bfs(graph::Graph{T}, source::T,\n destinations::Union{Set{T}, Vector{T}};\n reverse::Bool = false) where T\n\nReturns the Vector of nodes in the BFS path from the source (optionally, towards the destinations). If reverse=true returns the reverse order of nodes.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.shortest_path-Union{Tuple{T}, Tuple{Graph{T}, T, T}} where T","page":"The Graph object","title":"TenNetLib.shortest_path","text":"function shortest_path(graph::Graph{T}, source::T, destination::T) where T\n\nReturns the shortest path between source and destination in a Graph.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.nextnode_in_path-Union{Tuple{T}, Tuple{Graph{T}, T, T}, Tuple{Graph{T}, T, T, Any}} where T","page":"The Graph object","title":"TenNetLib.nextnode_in_path","text":"function nextnode_in_path(graph::Graph{T}, source::T, destination::T, n=1) where T\n\nReturns the next node in the shortest path between source and destination in a Graph. Optionally, finds nth next-node in the path.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.has_cycle-Union{Tuple{Graph{T}}, Tuple{T}} where T","page":"The Graph object","title":"TenNetLib.has_cycle","text":"function has_cycle(graph::Graph{T}) where T\n\nChecks whether a Graph has cycles/loops in it.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.find_sum_central_node-Union{Tuple{Graph{T}}, Tuple{T}, Tuple{Graph{T}, Union{Nothing, Set{T}}}} where T","page":"The Graph object","title":"TenNetLib.find_sum_central_node","text":"function find_sum_central_node(graph::Graph{T}) where T\nfunction find_sum_central_node(graph::Graph{T}, nodes::Set{T}) where T\nfunction find_sum_central_node(graph::Graph{T}, nodes::Vector{T}) where T\n\nFinds the sum central node node of a Graph. Optionally, when nodes is specified, finds the central node with respect to the nodes.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#TenNetLib.find_eccentric_central_node-Union{Tuple{Graph{T}}, Tuple{T}, Tuple{Graph{T}, Union{Nothing, Set{T}}}} where T","page":"The Graph object","title":"TenNetLib.find_eccentric_central_node","text":"function find_eccentric_central_node(graph::Graph{T}) where T\nfunction find_eccentric_central_node(graph::Graph{T}, nodes::Set{T}) where T\nfunction find_eccentric_central_node(graph::Graph{T}, nodes::Vector{T}) where T\n\nFinds the eccentric central node of a Graph. Optionally, when nodes is specified, finds the central node with respect to the nodes.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#Base.copy-Union{Tuple{Graph{T}}, Tuple{T}} where T","page":"The Graph object","title":"Base.copy","text":"function Base.copy(graph::Graph{T}) where T\n\nShallow copy of Graph.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#Base.getindex-Union{Tuple{T}, Tuple{Graph{T}, T}} where T","page":"The Graph object","title":"Base.getindex","text":"function Base.getindex(graph::Graph{T}, node::T) where T\n\nReturns the edges for a given node::T as an index. \n\n\n\n\n\n","category":"method"},{"location":"base/graph/#Base.setindex!-Union{Tuple{T}, Tuple{Graph{T}, Set{T}, T}} where T","page":"The Graph object","title":"Base.setindex!","text":"function Base.setindex!(graph::Graph{T}, neighbors::Set{T}, node::T) where T\nfunction Base.setindex!(graph::Graph{T}, neighbors::Vector{T}, node::T) where T\n\nSets the edges=neighbors for a given node::T as an index.\n\n\n\n\n\n","category":"method"},{"location":"base/graph/#Base.:==-Union{Tuple{T}, Tuple{Graph{T}, Graph{T}}} where T","page":"The Graph object","title":"Base.:==","text":"function Base.:(==)(graph1::Graph{T}, graph2::Graph{T}) where T\n\nEquality between two Graph objects.\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#OpStrings","page":"OpStrings","title":"OpStrings","text":"","category":"section"},{"location":"base/opstrings/","page":"OpStrings","title":"OpStrings","text":"TenNetLib.jl provides an alternative, called OpStrings, to ITensors.jl's OpSum to automatically construct Hamiltonains / operators. TenNetLib.jl's own CouplingModel is built from OpStrings and is not compatible with OpSum.","category":"page"},{"location":"base/opstrings/#OpString","page":"OpStrings","title":"OpString","text":"","category":"section"},{"location":"base/opstrings/","page":"OpStrings","title":"OpStrings","text":"OpStrings is basically a vector of OpString objects (notice the difference in 's' at the end)","category":"page"},{"location":"base/opstrings/","page":"OpStrings","title":"OpStrings","text":"OpString\nTenNetLib.coefficient(opstr::OpString)\noperators(opstr::OpString)\nminsite(opstr::OpString)\nmaxsite(opstr::OpString)\nremoveIds(opstr::OpString{T}) where {T <: Number}\nbosonize(opstr::OpString{T1}, sites::Vector{Index{T2}}) where {T1 <: Number, T2}","category":"page"},{"location":"base/opstrings/#TenNetLib.OpString","page":"OpStrings","title":"TenNetLib.OpString","text":"struct OpString{T <: Number}\n coeff::T\n ops::Vector{Pair{String, Int}}\nend\n\nHolds operator strings (operator names with corresponding positions) along with the coefficient.\n\ncoeff::T: Coeffcient of the operator string.\nops::Vector{Pair{String, Int}}: String of operator names along with the positions.\n\n\n\n\n\n","category":"type"},{"location":"base/opstrings/#TenNetLib.coefficient-Tuple{OpString}","page":"OpStrings","title":"TenNetLib.coefficient","text":"function coefficient(opstr::OpString)\n\nReturns the coefficient of the OpString.\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#TenNetLib.operators-Tuple{OpString}","page":"OpStrings","title":"TenNetLib.operators","text":"function operators(opstr::OpString)\n\nReturns the operator string of the OpString.\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#TenNetLib.minsite-Tuple{OpString}","page":"OpStrings","title":"TenNetLib.minsite","text":"function minsite(opstr::OpString)\n\nReturns the lowest site position in the operator string of the OpString.\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#TenNetLib.maxsite-Tuple{OpString}","page":"OpStrings","title":"TenNetLib.maxsite","text":"function maxsite(opstr::OpString)\n\nReturns the highest site position in the operator string of the OpString.\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#TenNetLib.removeIds-Union{Tuple{OpString{T}}, Tuple{T}} where T<:Number","page":"OpStrings","title":"TenNetLib.removeIds","text":"function removeIds(opstr::OpString{T}) where {T <: Number}\n\nReturns an OpString with all \"Id\" operators removed from the original.\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#TenNetLib.bosonize-Union{Tuple{T2}, Tuple{T1}, Tuple{OpString{T1}, Array{Index{T2}, 1}}} where {T1<:Number, T2}","page":"OpStrings","title":"TenNetLib.bosonize","text":"function bosonize(opstr::OpString{T1},\n sites::Vector{Index{T2}}) where {T1 <: Number, T2}\n\nReturns an OpString after \"bosonizing\" the original with Jordan-Wigner strings as needed. See bosonize.\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#OpStrings-2","page":"OpStrings","title":"OpStrings","text":"","category":"section"},{"location":"base/opstrings/","page":"OpStrings","title":"OpStrings","text":"OpStrings{T}\nremoveIdsZeros(os::OpStrings{T}) where {T <: Number}\nbosonize(os::OpStrings{T1}, sites::Vector{Index{T2}}) where {T1 <: Number, T2}\nmergeterms(os::OpStrings{T}) where T <: Number","category":"page"},{"location":"base/opstrings/#TenNetLib.OpStrings","page":"OpStrings","title":"TenNetLib.OpStrings","text":"const OpStrings{T} = Vector{OpString{T}}\n\nCollection of OpStrings.\n\nSyntax:\n\nos = OpStrings()\nos += 1, \"Sx\" => i, \"Sx\" => j, \"Sx\" => k, ....\nos += \"Sx\" => i, \"Sx\" => j, \"Sx\" => k, ....\n\nExample:\n\nos = OpStrings() \nfor j=1:N-1\n os += 1, \"Sz\" => j, \"Sz\" => j+1\n os += 0.5, \"S+\" => j, \"S-\" => j+1\n os += 0.5, \"S-\" => j, \"S+\" => j+1\nend\n\n\n\n\n\n","category":"type"},{"location":"base/opstrings/#TenNetLib.removeIdsZeros-Union{Tuple{Array{OpString{T}, 1}}, Tuple{T}} where T<:Number","page":"OpStrings","title":"TenNetLib.removeIdsZeros","text":"function removeIdsZeros(os::OpStrings{T}) where {T <: Number}\n\nReturns an OpStrings with all \"Id\" operators removed from the original, as well as any OpString term that has coeff less than Float64_threshold().\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#TenNetLib.bosonize-Union{Tuple{T2}, Tuple{T1}, Tuple{Array{OpString{T1}, 1}, Array{Index{T2}, 1}}} where {T1<:Number, T2}","page":"OpStrings","title":"TenNetLib.bosonize","text":"function bosonize(os::OpStrings{T1}, sites::Vector{Index{T2}}) where {T1 <: Number, T2}\n\nReturns an OpStrings after \"bosonizing\" the original with Jordan-Wigner strings as needed. See bosonize.\n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#TenNetLib.mergeterms-Union{Tuple{Array{OpString{T}, 1}}, Tuple{T}} where T<:Number","page":"OpStrings","title":"TenNetLib.mergeterms","text":"function mergeterms(os::OpStrings{T}) where T <: Number\n\nReturns an OpStrings where OpString elements with exactly same operator strings has been merged by adding the coefficients. \n\n\n\n\n\n","category":"method"},{"location":"base/opstrings/#MPO-from-OpStrings","page":"OpStrings","title":"MPO from OpStrings","text":"","category":"section"},{"location":"base/opstrings/","page":"OpStrings","title":"OpStrings","text":"ITensors.MPO(os::OpStrings{T1}, sites::Vector{Index{T2}}; maxdim::Int = typemax(Int), mindim::Int = 1, cutoff::Float64 = Float64_threashold(), svd_alg::String = \"divide_and_conquer\", chunksize::Int = 12) where {T1 <: Number, T2}","category":"page"},{"location":"base/opstrings/#ITensors.MPO-Union{Tuple{T2}, Tuple{T1}, Tuple{Array{OpString{T1}, 1}, Array{Index{T2}, 1}}} where {T1<:Number, T2}","page":"OpStrings","title":"ITensors.MPO","text":"function ITensors.MPO(os::OpStrings{T1},\n sites::Vector{Index{T2}};\n maxdim::Int = typemax(Int),\n mindim::Int = 1,\n cutoff::Float64 = Float64_threashold(),\n svd_alg::String = \"divide_and_conquer\",\n chunksize::Int = 12) where {T1 <: Number, T2}\n\nCreates MPO from os::OpStrings. The present version uses recursive SVDs to create the MPO. Very inefficient when number of Hamiltonian terms is large. Future updates will solve the problem.\n\nNamed arguments and their default values:\n\nmaxdim::Int = typemax(Int): Maximum MPO bond dimension after SVD truncation.\nmindim::Int = 1: Minimum MPO bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\nchunksize::Int = 12. Maximum size of the chunks on which recursive SVDs are performed.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_gen/#Generating-TTN","page":"Generating TTN","title":"Generating TTN","text":"","category":"section"},{"location":"ttn/ttn_gen/","page":"Generating TTN","title":"Generating TTN","text":"TenNetLib.jl defines following functions to generate TTNs with random entries.","category":"page"},{"location":"ttn/ttn_gen/","page":"Generating TTN","title":"Generating TTN","text":"For the standard TTN with the default hierarchical binary tree structure, follwoing function can be used.","category":"page"},{"location":"ttn/ttn_gen/","page":"Generating TTN","title":"Generating TTN","text":"default_randomTTN","category":"page"},{"location":"ttn/ttn_gen/#TenNetLib.default_randomTTN","page":"Generating TTN","title":"TenNetLib.default_randomTTN","text":"function default_randomTTN(sites::Vector{Index{T}}, chi::Int, qn::QN = QN()) where T\n\nReturns a TTN object, having random elements, from site Indexs sites, initial bond dimension chi and (optional) global QN sector qn. The structure is a default hierarchical binary tree graph. Automatically handles situations where the number of sites is not a power of 2.\n\nNote: For QN conserving TTN, the bond dimension might be off by one or two from chi.\n\n\n\n\n\n","category":"function"},{"location":"ttn/ttn_gen/","page":"Generating TTN","title":"Generating TTN","text":"The underlying default binary tree for the function above is generated by the following function.","category":"page"},{"location":"ttn/ttn_gen/","page":"Generating TTN","title":"Generating TTN","text":"default_graph_sitenodes(N::Int)","category":"page"},{"location":"ttn/ttn_gen/#TenNetLib.default_graph_sitenodes-Tuple{Int64}","page":"Generating TTN","title":"TenNetLib.default_graph_sitenodes","text":"function default_graph_sitenodes(N::Int)\n\nGiven the total number of sites, N::Int, generates the default hierarchical binary tree graph and a Dict{Int, Int2} object that maps each site to the corresponding node. Automatically handles situations where the number of sites is not a power of 2.\n\nReturn values:\n\n::Graph{Int2}: Default hierarchical tree graph to accomodate N number of sites in a TTN.\n::Dict{Int, Int2}: Maps each site to the corresponding node.\n\nExample:\n\ngraph, sitenodes = default_graph_sitenodes(32)\n\nsitenodes[1] == (1,1) # true\nsitenodes[2] == (1,1) # tru\nsitenodes[3] == (1,2) # true\nsitenodes[4] == (1,2) # true\nsitenodes[31] == (1,16) # true\nsitenodes[32] == (1,16) # true\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_gen/","page":"Generating TTN","title":"Generating TTN","text":"In the generic scenario, a random TTN with user-defined structure can be generated by the following function.","category":"page"},{"location":"ttn/ttn_gen/","page":"Generating TTN","title":"Generating TTN","text":"randomTTN","category":"page"},{"location":"ttn/ttn_gen/#TenNetLib.randomTTN","page":"Generating TTN","title":"TenNetLib.randomTTN","text":"function randomTTN(sites::Vector{Index{T}}, graph::Graph{Int2},\n sitenodes::Dict{Int, Int2}, chi::Int, qn::QN = QN()) where T\n\nReturns a TTN object, having random elements, from site Indexs sites, the underlyting graph, sitenodes::Dict{Int, Int2} that maps each site to the corresponding node, initial bond dimension chi, and (optional) global QN sector qn. The structure is determined by the input graph object.\n\nNote: This function can be used to generate any loop-free tensor network.\n\nNote: For QN conserving TTN, the bond dimension might be off by one or two from chi.\n\n\n\n\n\n","category":"function"},{"location":"ttn/ttn_gen/","page":"Generating TTN","title":"Generating TTN","text":"info: Info\nThe above function can be used to generate any loop-free tensor network.","category":"page"},{"location":"mps/example_dmrg/#Example:-DMRG","page":"Example: DMRG","title":"Example: DMRG","text":"","category":"section"},{"location":"mps/example_dmrg/#Ground-state-search","page":"Example: DMRG","title":"Ground state search","text":"","category":"section"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"A straight-forward DMRG can be performed as follows.","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"using ITensors\nusing TenNetLib\n\nlet\n N = 32\n sites = siteinds(\"S=1/2\",N)\n os = OpStrings()\n \n for j=1:N-1\n os += 1, \"Sz\" => j, \"Sz\" => j+1\n os += 0.5, \"S+\" => j, \"S-\" => j+1\n os += 0.5, \"S-\" => j, \"S+\" => j+1\n end\n \n H = CouplingModel(os,sites)\n states = [isodd(n) ? \"Up\" : \"Dn\" for n in 1:N]\n psi0 = MPS(sites, states)\n\n params = DMRGParams(;nsweeps = [10, 10], maxdim = [20, 50],\n cutoff = 1e-14, noise = 1e-3, noisedecay = 2,\n disable_noise_after = 5)\n\n # dmrg2 for two-site DMRG\n en, psi = dmrg2(psi0, H, params)\n\n # or dmrg1 for single-site DMRG\n # en, psi = dmrg1(psi0, H, params)\nend","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"Here, we have used OpStrings and CouplingModel. Alternatively, standard OpSum and MPO can be used.","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"Instead of using such higher-level code, one can also use lower-level functions for a better control.","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"sysenv = StateEnvs(psi0, H)\nnsite = 2 # two-site update\n\nswdata = dmrg!(sysenv, params, nsite)\n\n# Get energy from `Sweepdata`\nenergy = swdata.energy[end]\n\n# take a shallow copy of the MPS\n# if the `StateEnvs` will be updated later again\npsi = getpsi(sysenv)\n\n# Alternatively, take the psi from `StateEnvs` itself.\n# NOTE: This can crash the simulation, if the MPS is modified (e.g., in measurements)\n# and `StateEnvs` is going to be updated later on.\n# psi = sysenv.psi","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"Most often, it is better to do a single-site DMRG (without any noise) after standard two-site update for better convergence. Such lower-level function using StateEnvs is useful for that.","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"sysenv = StateEnvs(psi0, H)\n\nparams2 = DMRGParams(;nsweeps = [10, 10], maxdim = [20, 50],\n cutoff = 1e-14, noise = 1e-3, noisedecay = 2,\n disable_noise_after = 5)\ndmrg!(sysenv, params2, 2)\n\nparams1 = DMRGParams(;nsweeps = [10], maxdim = [50], cutoff = 0.0)\ndmrg!(sysenv, params1, 1)","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"Using such lower-level function, one can also restart the simulation at later times (e.g., by saving the StateEnvs using Serialization.jl), or one can perform updateH! to slowly change the Hamiltonian during DMRG simulations. Most often it is better to perform a ","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"Global Subspace Expansion can also be used to get rid of nasty local minimas (if needed), if the StateEnvs is built from a single MPO.","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"krylov_extend!(sysenv; extension_applyH_maxdim = 40)","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"warning: Warning\nGlobal Subspace Expansion may result into huge MPS bond dimension. That is why the named input parameters of krylov_extend! should be chosen carefully.","category":"page"},{"location":"mps/example_dmrg/#Excited-state-DMRG","page":"Example: DMRG","title":"Excited state DMRG","text":"","category":"section"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"Excited state DMRG is also straightforword.","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"# Given a ground state `psi_gr`, initial MPS `psi0`,\n# and a Hamiltonian `H`\n\n# dmrg2 for two-site DMRG\nen, psi = dmrg2(psi0, H, [psi_gr], params; weight = 10.0)\n\n# or dmrg1 for single-site DMRG\n# en, psi = dmrg1(psi0, H, [psi_gr], params; weight = 10.0)","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"Similarly, using StateEnvs:","category":"page"},{"location":"mps/example_dmrg/","page":"Example: DMRG","title":"Example: DMRG","text":"sysenv_ex = StateEnvs(psi0, H, [psi_gr]; weight = 10.0)\nnsite = 2 # two-site update\n\nswdata_ex = dmrg!(sysenv_ex, params, nsite)\n\n# Get energy from `Sweepdata`\nenergy1 = swdata_ex.energy[end]\n\n# take a shallow copy of the MPS\n# if the `StateEnvs` will be updated later again\npsi1 = getpsi(sysenv_ex)\n\n# Alternatively, take the psi from `StateEnvs` itself.\n# NOTE: This can crash the simulation, if the MPS is modified (e.g., in measurements)\n# and `StateEnvs` is going to be updated later.\n# psi1 = sysenv_ex.psi","category":"page"},{"location":"ttn/optimize_ttn/#Optimizing-TTN","page":"Optimizing TTN","title":"Optimizing TTN","text":"","category":"section"},{"location":"ttn/optimize_ttn/","page":"Optimizing TTN","title":"Optimizing TTN","text":"Functions to optimize TTN.","category":"page"},{"location":"ttn/optimize_ttn/#OptimizeParamsTTN","page":"Optimizing TTN","title":"OptimizeParamsTTN","text":"","category":"section"},{"location":"ttn/optimize_ttn/","page":"Optimizing TTN","title":"Optimizing TTN","text":"TenNetLib.jl defines a struct, called OptimizeParamsTTN, to control TTN optimizations.","category":"page"},{"location":"ttn/optimize_ttn/","page":"Optimizing TTN","title":"Optimizing TTN","text":"OptimizeParamsTTN\nOptimizeParamsTTN(;maxdim::Vector{Int}, nsweeps::Vector{Int}, cutoff::Union{Vector{Float64}, Float64} = _Float64_Threshold, noise::Union{Vector{Float64}, Float64, Int} = 0.0, noisedecay::Union{Vector{Float64}, Float64, Int} = 1.0, disable_noise_after::Union{Vector{Int}, Int} = typemax(Int))\nBase.copy(params::OptimizeParamsTTN)","category":"page"},{"location":"ttn/optimize_ttn/#TenNetLib.OptimizeParamsTTN","page":"Optimizing TTN","title":"TenNetLib.OptimizeParamsTTN","text":"mutable struct OptimizeParamsTTN\n maxdim::Vector{Int}\n nsweeps::Vector{Int}\n cutoff::Vector{Float64}\n noise::Vector{Float64}\n noisedecay::Vector{Float64}\n disable_noise_after::Vector{Int}\nend\n\nHolds parameters to control the optimzation sweeps of the TTN.\n\nmaxdim::Vector{Int}: Maximum allowed TTN bond/link dimensions at each stages of optimization.\nnsweeps::Vector{Int}: Number of sweeps to be performed at each statges of optimization.\ncutoff::Vector{Float64}: Cutoff for SVD truncation at each stages of optimization.\nnoise::Vector{Float64}: Noise level at each stages of optimization.\nnoisedecay::Vector{Float64}: Decay of noise level at each states of optimization.\n\nNoise is divided by noisedecay after each sweep.\n\ndisable_noise_after::Vector{Int}: Switch of noise after this many sweeps at each\n\nstates of optimization.\n\nAll these Vectors must have same dimension.\n\n\n\n\n\n","category":"type"},{"location":"ttn/optimize_ttn/#TenNetLib.OptimizeParamsTTN-Tuple{}","page":"Optimizing TTN","title":"TenNetLib.OptimizeParamsTTN","text":"function OptimizeParamsTTN(;maxdim::Vector{Int}, nsweeps::Vector{Int}, \n cutoff::Union{Vector{Float64}, Float64} = Float64_threshold(),\n noise::Union{Vector{Float64}, Float64, Int} = 0.0,\n noisedecay::Union{Vector{Float64}, Float64, Int} = 1.0,\n disable_noise_after::Union{Vector{Int}, Int} = typemax(Int))\n\nConstructor for OptimizeParamsTTN. Takes named arguments.\n\nmaxdim::Vector{Int}: Maximum allowed TTN bond/link dimensions at each stages of optimization.\nnsweeps::Vector{Int}: Number of sweeps to be performed at each statges of optimization.\ncutoff::Union{Float64, Vector{Float64}} = Float64_threshold(): Cutoff for SVD truncation at each stages of optimization. If Float64, cutoff remains same throughout the optimization simulation. \nnoise::Union{Float64, Int, Vector{Float64}} = 0.0: Noise level at each stages of optimization. If Float64 / Int, initial noise remains same throughout the optimization.\nnoisedecay::Union{Float64, Int, Vector{Float64}} = 1.0: Decay of noise level at each states of optimization. Noise is divided by noisedecay after each sweep. If Float64 / Int, noisedecay remains same throughout the DMRG simulation.\ndisable_noise_after::Union{Int, Vector{Int}} = typemax(Int): Switch of noise after this many sweeps at each states of optimization. If Int, disable_noise_after remains same throughout the optimization.\n\n\n\n\n\n","category":"method"},{"location":"ttn/optimize_ttn/#Base.copy-Tuple{OptimizeParamsTTN}","page":"Optimizing TTN","title":"Base.copy","text":"Base.copy(params::OptimizeParamsTTN)\n\nShallow copy OptimizeParamsTTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/optimize_ttn/#A-lower-level-optimization-function","page":"Optimizing TTN","title":"A lower level optimization function","text":"","category":"section"},{"location":"ttn/optimize_ttn/","page":"Optimizing TTN","title":"Optimizing TTN","text":"Following function modifies StateEnvsTTN in-place. Skip this function if you want to avoid lower-level abstraction.","category":"page"},{"location":"ttn/optimize_ttn/","page":"Optimizing TTN","title":"Optimizing TTN","text":"optimize!(sysenv::StateEnvsTTN, params::OptimizeParamsTTN,sweeppath::Vector{Int2}; kwargs...)","category":"page"},{"location":"ttn/optimize_ttn/#TenNetLib.optimize!-Tuple{StateEnvsTTN, OptimizeParamsTTN, Vector{Tuple{Int64, Int64}}}","page":"Optimizing TTN","title":"TenNetLib.optimize!","text":"function optimize!(sysenv::StateEnvsTTN,\n params::OptimizeParamsTTN,\n sweeppath::Vector{Int2};\n kwargs...)\n\nPerforms optimization of the TTN.\n\nArguments:\n\nsysenv::StateEnvsTTN.\nparams::OptimizationParamsTTN.\nsweeppath::Vector{Int2}: The path to be followed during optimization sweep. A vector that must contain all the nodes atleast once.\n\nNamed arguments and their default values:\n\nnormalize::Bool = true: Whether to normalize after update.\nsvd_alg::String = \"divide_and_conquer\".\nweight::Float64 = -1.0: Weight for the excited state calculation. Must be set to greater than 0 for the excited state optimization.\noutputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.\n\nConvergence criteria:\n\nenergyErrGoal: Optimization (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and the optimzation moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.\n\nNamed arguments for eig_solver and their default values:\n\nSee documentation of KrylovKit.jl.\n\nishermitian::Bool = true\nsolver_tol::Float64 = 1E-14.\nsolver_krylovdim::Int = 3.\nsolver_maxiter::Int = 1.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false.\nsolver_check_convergence::Bool = false.\n\nReturn values:\n\nSweepDataTTN\n\n\n\n\n\n","category":"method"},{"location":"ttn/optimize_ttn/#Higher-level-optimzation-functions","page":"Optimizing TTN","title":"Higher level optimzation functions","text":"","category":"section"},{"location":"ttn/optimize_ttn/","page":"Optimizing TTN","title":"Optimizing TTN","text":"optimize(psi0::TTN, H::CouplingModel, params::OptimizeParamsTTN, sweeppath::Vector{Int2}; kwargs...)","category":"page"},{"location":"ttn/optimize_ttn/#TenNetLib.optimize-Tuple{TTN, CouplingModel, OptimizeParamsTTN, Vector{Tuple{Int64, Int64}}}","page":"Optimizing TTN","title":"TenNetLib.optimize","text":"function optimize(psi0::TTN, H::CouplingModel,\n params::OptimizeParamsTTN,\n sweeppath::Vector{Int2};\n kwargs...)\n\nfunction optimize(psi0::TTN, H::CouplingModel, Ms::Vector{TTN},\n params::OptimizeParamsTTN,\n sweeppath::Vector{Int2};\n kwargs...)\n\nPerforms optimization of the TTN.\n\nArguments:\n\npsi0::TTN: Initial TTN.\nH::CouplingModel, Ms::Vector{MPS}.\nparams::OptimizationParamsTTN.\nsweeppath::Vector{Int2}: The path to be followed during optimization sweep. A vector that must contain all the nodes atleast once.\n\nNamed arguments and their default values:\n\nnormalize::Bool = true: Whether to normalize after update.\nsvd_alg::String = \"divide_and_conquer\".\nweight::Float64 = -1.0: Weight for the excited state calculation. Must be set to greater than 0 for the excited state optimization.\noutputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.\n\nConvergence criteria:\n\nenergyErrGoal: Optimization (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and the optimzation moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.\n\nNamed arguments for eig_solver and their default values:\n\nSee documentation of KrylovKit.jl.\n\nishermitian::Bool = true\nsolver_tol::Float64 = 1E-14.\nsolver_krylovdim::Int = 3.\nsolver_maxiter::Int = 1.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false.\nsolver_check_convergence::Bool = false.\n\nReturn values:\n\n::Float64: Energy.\n::TTN: The state psi.\n\n\n\n\n\n","category":"method"},{"location":"base/global/#Controlling-global-behaviors","page":"Controlling global behaviors","title":"Controlling global behaviors","text":"","category":"section"},{"location":"base/global/","page":"Controlling global behaviors","title":"Controlling global behaviors","text":"TenNetLib.jl provides following functions to control global behaviors for Tensor Network simulations.","category":"page"},{"location":"base/global/","page":"Controlling global behaviors","title":"Controlling global behaviors","text":"Float64_threshold\nusing_threaded_loop\nenable_threaded_loop\ndisable_threaded_loop\n@threaded_loop","category":"page"},{"location":"base/global/#TenNetLib.Float64_threshold","page":"Controlling global behaviors","title":"TenNetLib.Float64_threshold","text":"function Float64_threshold()\nfunction Float64_threshold(threshold::Float)\n\nReturns threshold for floating point calculations. In most places, any number below this will be treated zero. E.g., in cutoff. Default: 1e-15.\n\nOptionally, change the threshold as per the input threshold.\n\n\n\n\n\n","category":"function"},{"location":"base/global/#TenNetLib.using_threaded_loop","page":"Controlling global behaviors","title":"TenNetLib.using_threaded_loop","text":"function using_threaded_loop()\n\nReturns the condition whether to use threaded loop in inbuild TeNLib functions.\n\n\n\n\n\n","category":"function"},{"location":"base/global/#TenNetLib.enable_threaded_loop","page":"Controlling global behaviors","title":"TenNetLib.enable_threaded_loop","text":"function enable_threaded_loop()\n\nEnable the use of threaded loop in inbuild TeNLib functions.\n\n\n\n\n\n","category":"function"},{"location":"base/global/#TenNetLib.disable_threaded_loop","page":"Controlling global behaviors","title":"TenNetLib.disable_threaded_loop","text":"function disable_threaded_loop()\n\nDisable the use of threaded loop in inbuild TeNLib functions.\n\n\n\n\n\n","category":"function"},{"location":"base/global/#TenNetLib.@threaded_loop","page":"Controlling global behaviors","title":"TenNetLib.@threaded_loop","text":"macro threaded_loop(code)\n\nConditional threaded loop by Threads.@threads. If using_threaded_loop() returns true, performs parallel loop, otherwise performs serial loop.\n\nNote: All other forms of parallelization are switched off inside the loop body, if parallel loop is being executed.\n\nExample:\n\n@threaded_loop for i = 1 : N\n # Do stuff in parallel\nend\n\n\n\n\n\n","category":"macro"},{"location":"ttn/sweep_ttn/#Sweeping-through-the-TTN","page":"Sweeping through the TTN","title":"Sweeping through the TTN","text":"","category":"section"},{"location":"ttn/sweep_ttn/","page":"Sweeping through the TTN","title":"Sweeping through the TTN","text":"At a lower level of abstraction, TenNetLib.jl allows to control each fullsweep manually to update StateEnvsTTN.","category":"page"},{"location":"ttn/sweep_ttn/","page":"Sweeping through the TTN","title":"Sweeping through the TTN","text":"Skip this part if you want to avoid lower-level abstraction.","category":"page"},{"location":"ttn/sweep_ttn/#SweepDataTTN","page":"Sweeping through the TTN","title":"SweepDataTTN","text":"","category":"section"},{"location":"ttn/sweep_ttn/","page":"Sweeping through the TTN","title":"Sweeping through the TTN","text":"TenNetLib.jl defines a struct, called SweepDataTTN, to store essential data after each fullsweep.","category":"page"},{"location":"ttn/sweep_ttn/","page":"Sweeping through the TTN","title":"Sweeping through the TTN","text":"SweepDataTTN\nBase.copy(swdata::SweepDataTTN)","category":"page"},{"location":"ttn/sweep_ttn/#TenNetLib.SweepDataTTN","page":"Sweeping through the TTN","title":"TenNetLib.SweepDataTTN","text":"mutable struct SweepDataTTN\n sweepcount::Int\n maxchi::Vector{Int}\n energy::Vector{Float64}\nend\n\nHolds historical data after each (full)sweep of the TTN. Requires for convergence check etc.\n\nsweepcount::Int: Number of fullsweeps performed.\nmaxchi::Vector{Int}: Maximum MPS bond/link dimensions after every sweep.\nenergy::Vector{Float64}: Energies after every sweep.\n\nDefault constructor:\n\nSweepDataTTN(): Initialize an empty SweepData object.\n\n\n\n\n\n","category":"type"},{"location":"ttn/sweep_ttn/#Base.copy-Tuple{SweepDataTTN}","page":"Sweeping through the TTN","title":"Base.copy","text":"Base.copy(swdata::SweepDataTTN)\n\nShallow copy of SweepDataTTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/sweep_ttn/#sweeppath","page":"Sweeping through the TTN","title":"sweeppath","text":"","category":"section"},{"location":"ttn/sweep_ttn/","page":"Sweeping through the TTN","title":"Sweeping through the TTN","text":"default_sweeppath","category":"page"},{"location":"ttn/sweep_ttn/#TenNetLib.default_sweeppath","page":"Sweeping through the TTN","title":"TenNetLib.default_sweeppath","text":"function default_sweeppath(psi::TTN)\n\nFor a given a TTN having the default hierarchical binary tree structure, teturns the default path for sweeping through the TTN.\n\nReturn values:\n\nVector{Int2}: The list of nodes as the path to be followed during a (half)sweep.\n\n\n\n\n\n","category":"function"},{"location":"ttn/sweep_ttn/#Perform-a-fullsweep","page":"Sweeping through the TTN","title":"Perform a fullsweep","text":"","category":"section"},{"location":"ttn/sweep_ttn/","page":"Sweeping through the TTN","title":"Sweeping through the TTN","text":"fullsweep!(sysenv::StateEnvsTTN, sweeppath::Vector{Int2}, solver, swdata::SweepDataTTN; kwargs...)","category":"page"},{"location":"ttn/sweep_ttn/#TenNetLib.fullsweep!-Tuple{StateEnvsTTN, Vector{Tuple{Int64, Int64}}, Any, SweepDataTTN}","page":"Sweeping through the TTN","title":"TenNetLib.fullsweep!","text":"function fullsweep!(sysenv::StateEnvsTTN, sweeppath::Vector{Int2}, solver,\n swdata::SweepDataTTN; kwargs...)\n\nPerform a fullsweep of the TTN by solver.\n\nArguments:\n\nsysenv::StateEnvsTTN.\nsweeppath::Vector{Int2}: The list of nodes as the path to be followed during a (half)sweep. Must have each node atleast once. For the next halfsweep the reverse path is followed.\nsolver: Solver for update. Currently only eig_solver is supported.\nswdata::SweepDataTTN.\n\nNamed arguments and their default values:\n\ntime_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for future functionality.\nnormalize::Bool = true: Whether to normalize after update.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\nnoise::Float64 = 0.0.\nexpand_dim::Int = 0 if noise == 0 else 20. Dimension to be expanded (on top of maxdim) during subspace expansion.\nmax_expand_dim::Int = 2 * expand_dim. maximum dimension to be expanded during subspace expansion.\nexpand_numiter::Int = 4. Number of iteration for subspace expansion. Should be greater than 1.\nlinkwise_maxdim::Union{Nothing, Dict{LinkTypeTTN, Int}} = nothing. Specifies maximum bond dimension of a particular link. \noutputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true.\nsolver_tol::Float64 = 1E-14.\nsolver_krylovdim::Int = 5.\nsolver_maxiter::Int = 2.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false.\nsolver_check_convergence::Bool = false.\n\nReturn values:\n\n::Float64: Change in Energy ΔE\n\nswdata::SweepDataTTN gets updated.\n\n\n\n\n\n","category":"method"},{"location":"base/solver/#Solvers","page":"Solvers","title":"Solvers","text":"","category":"section"},{"location":"base/solver/","page":"Solvers","title":"Solvers","text":"Functions to perform local updates. These functions use Krylovkit.jl.","category":"page"},{"location":"base/solver/","page":"Solvers","title":"Solvers","text":"eig_solver\nexp_solver","category":"page"},{"location":"base/solver/#TenNetLib.eig_solver","page":"Solvers","title":"TenNetLib.eig_solver","text":"function eig_solver(env, phi0::ITensor, time_step::Nothing; kwargs...)\n\nSolver to find smallest eigenvalue corresponding to \"matrix\" env and input vector phi0.\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true\nsolver_tol::Float64 = 1E-14.\nsolver_krylovdim::Int = 5.\nsolver_maxiter::Int = 2.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false.\nsolver_check_convergence::Bool = false.\n\nReturn values:\n\n::Float64: Smallest eigenvalue.\n::ITensor: Eigenstate corresponding to the smallest eigenvalue.\n\n\n\n\n\n","category":"function"},{"location":"base/solver/#TenNetLib.exp_solver","page":"Solvers","title":"TenNetLib.exp_solver","text":"function exp_solver(env, phi0::ITensor, time_step::Union{Float64, ComplexF64}; kwargs...)\n\nExponentiation solver to find exp(env * phi0 * time_step).\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true\nsolver_tol::Float64 = 1E-12.\nsolver_krylovdim::Int = 30.\nsolver_maxiter::Int = 10.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = true.\nsolver_check_convergence::Bool = true.\n\nReturn values:\n\n::Float64: NaN. \n::ITensor: Exponentiated ITensor.\n\n\n\n\n\n","category":"function"},{"location":"ttn/update_site_ttn/#Perform-local-updates","page":"Perform local updates","title":"Perform local updates","text":"","category":"section"},{"location":"ttn/update_site_ttn/","page":"Perform local updates","title":"Perform local updates","text":"At the lowest-level of abstraction, TenNetLib.jl allows for updating the StateEnvsTTN for each sites manually.","category":"page"},{"location":"ttn/update_site_ttn/","page":"Perform local updates","title":"Perform local updates","text":"Skip this part if you want to avoid lower-level abstraction.","category":"page"},{"location":"ttn/update_site_ttn/","page":"Perform local updates","title":"Perform local updates","text":"update_position!(sysenv::StateEnvsTTN, solver, node::Int2; time_step::Union{Float64, ComplexF64, Nothing}, normalize::Bool, maxdim::Int, mindim::Int, cutoff::Float64, svd_alg::String, kwargs...)","category":"page"},{"location":"ttn/update_site_ttn/#TenNetLib.update_position!-Tuple{StateEnvsTTN, Any, Tuple{Int64, Int64}}","page":"Perform local updates","title":"TenNetLib.update_position!","text":"function update_position!(sysenv::StateEnvsTTN, solver, node::Int2;\n time_step::Union{Float64, ComplexF64, Nothing},\n normalize::Bool,\n maxdim::Int,\n mindim::Int,\n cutoff::Float64,\n svd_alg::String,\n kwargs...)\n\nMoves the orthogonality center to pos and update StateEnvsTTN at position pos by solver.\n\nArguments:\n\nsysenv::StateEnvsTTN\nsolver: Solver for update. Currently only eig_solver is supported.\npos::Int: Position of the node to be updated.\n\nNamed arguments and their default values:\n\ntime_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for future functionality.\nnormalize::Bool = true: Whether to normalize after update.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true.\nsolver_tol::Float64 = 1E-14.\nsolver_krylovdim::Int = 5.\nsolver_maxiter::Int = 2.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false.\nsolver_check_convergence::Bool = false.\n\nReturn values:\n\n::Float64: Energy.\n\n\n\n\n\n","category":"method"},{"location":"ttn/update_site_ttn/","page":"Perform local updates","title":"Perform local updates","text":"TenNetLib.jl implements the subspace expansion method described in SciPost Phys. Lect. Notes 8 (2019) to increase the bond dimension between two neighboring nodes.","category":"page"},{"location":"ttn/update_site_ttn/","page":"Perform local updates","title":"Perform local updates","text":"subspace_expand!(psi::TTN, node::Int2, nextnode::Int2, max_expand_dim::Int, noise::Float64)","category":"page"},{"location":"ttn/update_site_ttn/#TenNetLib.subspace_expand!-Tuple{TTN, Tuple{Int64, Int64}, Tuple{Int64, Int64}, Int64, Float64}","page":"Perform local updates","title":"TenNetLib.subspace_expand!","text":"function subspace_expand!(psi::TTN, node::Int2, nextnode::Int2,\n max_expand_dim::Int, noise::Float64)\n\nEnlarges the bond domension between node and nextnode by max_expand_dim using the subspace expansion. The parameter noise controls stength of the perturbation.\n\n\n\n\n\n","category":"method"},{"location":"base/couplingmodel/#CouplingModel","page":"CouplingModel","title":"CouplingModel","text":"","category":"section"},{"location":"base/couplingmodel/","page":"CouplingModel","title":"CouplingModel","text":"TenNetLib.jl degines as struct, called the CouplingModel, to store the Hamiltonian terms. In case of MPS based algorithms, CouplingModel can replace MPO without modifying rest of the code. For Tree Tensor Network (TTN) codes, only CouplingModel can be used. Different elements of CouplingModel are contracted in parallel.","category":"page"},{"location":"base/couplingmodel/","page":"CouplingModel","title":"CouplingModel","text":"CouplingModel\nCouplingModel(os::OpStrings{T1}, sites::Vector{Index{T2}}; merge::Bool = true,maxdim::Int = typemax(Int), mindim::Int = 1, cutoff::Float64 = Float64_threashold(),svd_alg::String = \"divide_and_conquer\", chunksize::Int = 12) where {T1 <: Number, T2}\nCouplingModel(os::OpStrings{T1}, mpo::MPO; merge::Bool = true,maxdim::Int = typemax(Int), mindim::Int = 1, cutoff::Float64 = Float64_threashold(),svd_alg::String = \"divide_and_conquer\", chunksize::Int = 12) where {T1 <: Number}\nCouplingModel(mpos::MPO...)\nBase.length(model::CouplingModel)\nBase.copy(model::CouplingModel)\nBase.getindex(model::CouplingModel, n)\nITensors.siteinds(model::CouplingModel)","category":"page"},{"location":"base/couplingmodel/#TenNetLib.CouplingModel","page":"CouplingModel","title":"TenNetLib.CouplingModel","text":"struct CouplingModel{T}\n sites::Vector{Index{T}}\n terms::Vector{IDTensors}\nend\n\nCouplingModel for a given OpStrings Hamiltonian terms and sites::Vector{Index}.\n\nsites::Vector{Index{T}}: Site Indexs.\nterms::Vector{IDTensors}: Collection of Hamiltonian terms. \n\n\n\n\n\n","category":"type"},{"location":"base/couplingmodel/#TenNetLib.CouplingModel-Union{Tuple{T2}, Tuple{T1}, Tuple{Array{OpString{T1}, 1}, Array{Index{T2}, 1}}} where {T1<:Number, T2}","page":"CouplingModel","title":"TenNetLib.CouplingModel","text":"function CouplingModel(os::OpStrings{T1},\n sites::Vector{Index{T2}};\n merge::Bool = true,\n maxdim::Int = typemax(Int),\n mindim::Int = 1,\n cutoff::Float64 = Float64_threashold(),\n svd_alg::String = \"divide_and_conquer\",\n chunksize::Int = 12) where {T1 <: Number, T2}\n\nConstructor of the CouplingModel from os::OpStrings and sites::Vector{Index}.\n\nNamed arguments and their default values:\n\nmerge::Bool = true. If true, merges all the terms having same spatial support resulting in larger virtual dimension. Otherwise, all the terms have virtual dimension one.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_Threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\nchunksize::Int = 12.\n\nExample:\n\nos = OpStrings() \nfor j=1:N-1\n os += 1, \"Sz\" => j, \"Sz\" => j+1\n os += 0.5, \"S+\" => j, \"S-\" => j+1\n os += 0.5, \"S-\" => j, \"S+\" => j+1\nend \nH = CouplingModel(os,sites)\n\n\n\n\n\n","category":"method"},{"location":"base/couplingmodel/#TenNetLib.CouplingModel-Union{Tuple{T1}, Tuple{Array{OpString{T1}, 1}, MPO}} where T1<:Number","page":"CouplingModel","title":"TenNetLib.CouplingModel","text":"function CouplingModel(os::OpStrings{T1},\n mpo::MPO;\n merge::Bool = true,\n maxdim::Int = typemax(Int),\n mindim::Int = 1,\n cutoff::Float64 = Float64_threashold(),\n svd_alg::String = \"divide_and_conquer\",\n chunksize::Int = 12) where {T1 <: Number}\n\nConstructor of the CouplingModel from os::OpStrings and mpo::MPO. Resultant CouplingModel is the sum of os and the mpo.\n\nNamed arguments and their default values:\n\nmerge::Bool = true. If true, merges all the terms having same spatial support resulting in larger virtual dimension. Otherwise, all the terms have virtual dimension one.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_Threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\nchunksize::Int = 12.\n\n\n\n\n\n","category":"method"},{"location":"base/couplingmodel/#TenNetLib.CouplingModel-Tuple{Vararg{MPO}}","page":"CouplingModel","title":"TenNetLib.CouplingModel","text":"function CouplingModel(mpos::MPO...)\n\nConstructs CouplingModel from a collection of MPOs. Different MPO terms are contracted in parallel. Useful for TTN codes.\n\n\n\n\n\n","category":"method"},{"location":"base/couplingmodel/#Base.length-Tuple{CouplingModel}","page":"CouplingModel","title":"Base.length","text":"function Base.length(model::CouplingModel)\n\nNumber of sites in the system.\n\n\n\n\n\n","category":"method"},{"location":"base/couplingmodel/#Base.copy-Tuple{CouplingModel}","page":"CouplingModel","title":"Base.copy","text":"function Base.copy(model::CouplingModel)\n\nShallow copy of CouplingModel.\n\n\n\n\n\n","category":"method"},{"location":"base/couplingmodel/#Base.getindex-Tuple{CouplingModel, Any}","page":"CouplingModel","title":"Base.getindex","text":"function Base.getindex(model::CouplingModel, n)\n\nReturns Hamiltonian terms for nth site(s) in the CouplingModel.\n\n\n\n\n\n","category":"method"},{"location":"base/couplingmodel/#ITensors.siteinds-Tuple{CouplingModel}","page":"CouplingModel","title":"ITensors.siteinds","text":"function ITensors.siteinds(model::CouplingModel)\n\nReturns the site Indexs of the CouplingModel.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#Performing-TDVP","page":"Performing TDVP","title":"Performing TDVP","text":"","category":"section"},{"location":"mps/tdvp/#TDVPEngine","page":"Performing TDVP","title":"TDVPEngine","text":"","category":"section"},{"location":"mps/tdvp/","page":"Performing TDVP","title":"Performing TDVP","text":"TenNetLib.jl defines a struct, called TDVPEngine, to store essential data during TDVP sweeps.","category":"page"},{"location":"mps/tdvp/","page":"Performing TDVP","title":"Performing TDVP","text":"TDVPEngine\nTDVPEngine(psi::MPS, H::T) where T <: Union{MPO, Vector{MPO}, CouplingModel}\nTDVPEngine(psi::MPS, H::T, Ms::Vector{MPS}; weight::Float64) where T <: Union{MPO, Vector{MPO}, CouplingModel}\ngetpsi(engine::TDVPEngine)\nsweepcount(engine::TDVPEngine)\ngetenergy(engine::TDVPEngine)\ngetentropy(engine::TDVPEngine)\nmaxchi(engine::TDVPEngine)\ntotalerror(engine::TDVPEngine)\nsweeperror(engine::TDVPEngine)\nkrylov_extend!(engine::TDVPEngine{ProjMPO}; kwargs...)\nsweepdata(engine::TDVPEngine)\nabstime(engine::TDVPEngine)\nupdateH!(engine::TDVPEngine, H::T; recalcEnv::Bool = true) where T <: Union{MPO, Vector{MPO}, CouplingModel}\nupdateH!(engine::TDVPEngine, H::T, Ms::Vector{MPS}; weight::Float64, recalcEnv::Bool = true) where T <: Union{MPO, Vector{MPO}, CouplingModel}\nBase.copy(engine::TDVPEngine)","category":"page"},{"location":"mps/tdvp/#TenNetLib.TDVPEngine","page":"Performing TDVP","title":"TenNetLib.TDVPEngine","text":"mutable struct TDVPEngine{T <: Union{ProjMPO,\n ProjMPOSum2,\n ProjMPO_MPS2,\n ProjMPOSum_MPS,\n ProjCouplingModel,\n ProjCouplingModel_MPS}}\n\nHolds the MPS state, SweepData, and absolute elpased time for TDVP simulations.\n\nsysenv::StateEnvs: Holds the state psi and environments PH.\nswdata::SweepData: Holds the historical data after each (full)sweep.\nabstime::Float64: Absolute elapsed time.\n\n\n\n\n\n","category":"type"},{"location":"mps/tdvp/#TenNetLib.TDVPEngine-Union{Tuple{T}, Tuple{MPS, T}} where T<:Union{MPO, CouplingModel, Vector{MPO}}","page":"Performing TDVP","title":"TenNetLib.TDVPEngine","text":"function TDVPEngine(psi::MPS, H::{T}) where T <: Union{MPO, Vector{MPO}, CouplingModel}\n\nConstructor of the TDVPEngine from different forms of Hamiltonians.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.TDVPEngine-Union{Tuple{T}, Tuple{MPS, T, Vector{MPS}}} where T<:Union{MPO, CouplingModel, Vector{MPO}}","page":"Performing TDVP","title":"TenNetLib.TDVPEngine","text":"function TDVPEngine(psi::MPS, H::T, Ms::Vector{MPS};\n weight::Float64) where T <: Union{MPO, Vector{MPO}, CouplingModel}\n\nConstructor of TDVPEngine from different forms of Hamiltonians and a vector of MPS.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.getpsi-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.getpsi","text":"function getpsi(engine::TDVPEngine)\n\nReturns (shallow copy of) the state psi.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.sweepcount-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.sweepcount","text":"function sweepcount(engine::TDVPEngine)\n\nReturns the number of sweeps performed.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.getenergy-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.getenergy","text":"function getenergy(engine::TDVPEngine)\n\nReturns the energy of the state psi.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.getentropy-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.getentropy","text":"function getentropy(engine::TDVPEngine)\n\nReturns the mid-chain entropy of the state psi.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.maxchi-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.maxchi","text":"function maxchi(engine::TDVPEngine)\n\nReturns the maximum bond/link dimension of the state psi.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.totalerror-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.totalerror","text":"function totalerror(engine::TDVPEngine)\n\nReturns the sum of the truncation errors of all the sweeps performed.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.sweeperror-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.sweeperror","text":"function sweeperror(engine::TDVPEngine)\n\nReturns the truncation error in the last sweep.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.krylov_extend!-Tuple{TDVPEngine{ProjMPO}}","page":"Performing TDVP","title":"TenNetLib.krylov_extend!","text":"function krylov_extend!(engine::TDVPEngine{ProjMPO}; kwargs...)\n\nPerforms Global Subspace Expansion.\n\nArguments and their default values:\n\nextension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.\nextension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.\nextension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.\nextension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.sweepdata-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.sweepdata","text":"function sweepdata(engine::TDVPEngine)\n\nReturns the (shallow copy of) SweepData.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.abstime-Tuple{TDVPEngine}","page":"Performing TDVP","title":"TenNetLib.abstime","text":"function abstime(engine::TDVPEngine)\n\nReturns the absolute elapsed time.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.updateH!-Union{Tuple{T}, Tuple{TDVPEngine, T}} where T<:Union{MPO, CouplingModel, Vector{MPO}}","page":"Performing TDVP","title":"TenNetLib.updateH!","text":"function updateH!(engine::TDVPEngine, H::T;\n recalcEnv::Bool = true) where T <: Union{MPO, Vector{MPO}, CouplingModel}\n\nUpdate Hamiltonian H in engine::TDVPEngine. If recalcEnv = false, it reuses previous environments. recalcEnv = false is only defined when the TDVPEngine is created from a single MPO.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#TenNetLib.updateH!-Union{Tuple{T}, Tuple{TDVPEngine, T, Vector{MPS}}} where T<:Union{MPO, CouplingModel, Vector{MPO}}","page":"Performing TDVP","title":"TenNetLib.updateH!","text":"function updateH!(engine::TDVPEngine, H::T, Ms::Vector{MPS};\n weight::Float64,\n recalcEnv::Bool = true) where T <: Union{MPO, Vector{MPO}, CouplingModel}\n\nUpdate Hamiltonian H in engine::TDVPEngine. recalcEnv = false is not supported.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#Base.copy-Tuple{TDVPEngine}","page":"Performing TDVP","title":"Base.copy","text":"Base.copy(engine::TDVPEngine)\n\nShallow copy of TDVPEngine.\n\n\n\n\n\n","category":"method"},{"location":"mps/tdvp/#tdvpsweep!","page":"Performing TDVP","title":"tdvpsweep!","text":"","category":"section"},{"location":"mps/tdvp/","page":"Performing TDVP","title":"Performing TDVP","text":"Following function performs one TDVP sweep.","category":"page"},{"location":"mps/tdvp/","page":"Performing TDVP","title":"Performing TDVP","text":"tdvpsweep!","category":"page"},{"location":"mps/tdvp/#TenNetLib.tdvpsweep!","page":"Performing TDVP","title":"TenNetLib.tdvpsweep!","text":"tdvpsweep!(engine::TDVPEngine, time_step::Union{Float64, ComplexF64}; \n nsite::Union{Int, String} = \"dynamic\", \n solver = exp_solver,\n kwargs...)::Nothing\n\nPerforms one TDVP sweep. Computes ψ' = exp(time_step * H) * ψ. Therefore, for real-time dynamics with step dt, time_step should be -im * dt. \n\nArguments:\n\nengine::TDVPEngine.\ntime_step::Union{Float64, ComplexF64}.\nnsite::Union{Int, String} = \"dynamic\": For two or one site sweeps, nsite=2 or nsite=1 respectively. For nsite=\"dynamic\", dynamic_fullsweep! is performed.\nsolver = exp_solver: Only exp_solver is supported now.\n\nNamed arguments and their default values:\n\nnormalize::Bool = true: Whether to normalize after update.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\noutputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.\neigthreshold::Float64 = 1E-12. Only applicable for nsite = \"dynamic\" (see dynamic_fullsweep!).\nextendat::Union{Nothing, Int} = nothing: If specified, at every extendatth sweep, Global Subspace Expansion is performed followed by a pure one-site sweep if typeof(sysenv) == StateEnvs{ProjMPO}, else performs a full two-site sweep. Only applicable for nsite = \"dynamic\" (see dynamic_fullsweep!).\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true.\nsolver_tol::Float64 = 1E-12.\nsolver_krylovdim::Int = 30.\nsolver_maxiter::Int = 100.\nsolver_outputlevel::Int = 0.: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = true.\nsolver_check_convergence::Bool = true.\n\nArguments for Global Subspace Expansion and their default values:\n\nOnly applicable for nsite = \"dynamic\" (see dynamic_fullsweep!).\n\nextension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.\nextension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.\nextension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.\nextension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.\n\n\n\n\n\n","category":"function"},{"location":"ttn/state_envs_ttn/#StateEnvsTTN:-A-container-to-store-the-TTN-and-its-environments","page":"StateEnvsTTN","title":"StateEnvsTTN: A container to store the TTN and its environments","text":"","category":"section"},{"location":"ttn/state_envs_ttn/","page":"StateEnvsTTN","title":"StateEnvsTTN","text":"Similar to the setup for MPS, tt the lowest-level of abstraction, TenNetLib.jl defines StateEnvs to hold a TTN and its environments to be modified in place.","category":"page"},{"location":"ttn/state_envs_ttn/","page":"StateEnvsTTN","title":"StateEnvsTTN","text":"Skip this part if you want to avoid lower-level abstraction.","category":"page"},{"location":"ttn/state_envs_ttn/","page":"StateEnvsTTN","title":"StateEnvsTTN","text":"StateEnvsTTN\nStateEnvsTTN(psi::TTN, M::CouplingModel)\nStateEnvsTTN(psi::TTN,M::CouplingModel,psis::Vector{TTN}; weight::Float64)\ngetpsi(sysenv::StateEnvsTTN)\ngetenv(sysenv::StateEnvsTTN)\nposition!(sysenv::StateEnvsTTN, node::Int2; maxdim::Int = typemax(Int), mindim::Int = 1, cutoff::Float64 = Float64_threshold(), svd_alg::String = \"divide_and_conquer\", normalize::Bool = false, node_to_skip::Union{Int2, Nothing} = nothing)\nTenNetLib.product(sysenv::StateEnvsTTN, v::ITensor)\nBase.copy(sysenv::StateEnvsTTN)","category":"page"},{"location":"ttn/state_envs_ttn/#TenNetLib.StateEnvsTTN","page":"StateEnvsTTN","title":"TenNetLib.StateEnvsTTN","text":"mutable struct StateEnvsTTN{T1, T2 <: Union{EnvCouplingModelTTN,\n EnvCouplingModelProjTTN}}\n psi::TTN{T1}\n env::T{T2}\nend\n\nHolds the TTN and the environment.\n\n\n\n\n\n","category":"type"},{"location":"ttn/state_envs_ttn/#TenNetLib.StateEnvsTTN-Tuple{TTN, CouplingModel}","page":"StateEnvsTTN","title":"TenNetLib.StateEnvsTTN","text":"function StateEnvsTTN(psi::TTN, H::CouplingModel)\n\nConstructor of the StateEnvsTTN from a CouplingModel. Each terms in the CouplingModel are contracted in parallel.\n\n\n\n\n\n","category":"method"},{"location":"ttn/state_envs_ttn/#TenNetLib.StateEnvsTTN-Tuple{TTN, CouplingModel, Vector{TTN}}","page":"StateEnvsTTN","title":"TenNetLib.StateEnvsTTN","text":"function StateEnvsTTN(psi::TTN, H::CouplingModel, Ms::Vector{TTN}; weight::Float64)\n\nConstructor of StateEnvsTTN from a CouplingModel and a vector of TTN used for excited state search. Each terms in the CouplingModel are contracted in parallel.\n\n\n\n\n\n","category":"method"},{"location":"ttn/state_envs_ttn/#TenNetLib.getpsi-Tuple{StateEnvsTTN}","page":"StateEnvsTTN","title":"TenNetLib.getpsi","text":"function getpsi(sysenv::StateEnvsTTN)\n\nReturns (shallow copy of) the state psi.\n\n\n\n\n\n","category":"method"},{"location":"ttn/state_envs_ttn/#TenNetLib.getenv-Tuple{StateEnvsTTN}","page":"StateEnvsTTN","title":"TenNetLib.getenv","text":"function getenv(sysenv::StateEnvsTTN)\n\nReturns (shallow copy of) the environment env.\n\n\n\n\n\n","category":"method"},{"location":"ttn/state_envs_ttn/#ITensors.position!-Tuple{StateEnvsTTN, Tuple{Int64, Int64}}","page":"StateEnvsTTN","title":"ITensors.position!","text":"function position!(sysenv::StateEnvsTTN, node::Int2;\n maxdim::Int = typemax(Int),\n mindim::Int = 1,\n cutoff::Float64 = _Float64_Threshold,\n svd_alg::String = \"divide_and_conquer\",\n normalize::Bool = true)\n\nMoves the orthogonality center of the TTN to node and updates the effective Hamiltonian of the same.\n\nNamed arguments and their default values:\n\nnormalize::Bool = true: Whether to normalize afterwards.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\n\n\n\n\n\n","category":"method"},{"location":"ttn/state_envs_ttn/#TenNetLib.product-Tuple{StateEnvsTTN, ITensor}","page":"StateEnvsTTN","title":"TenNetLib.product","text":"function product(sysenv::StateEnvsTTN, v::ITensor)\n\nReturns the Matrix-Vector product between the environment and input ITensor v.\n\n\n\n\n\n","category":"method"},{"location":"ttn/state_envs_ttn/#Base.copy-Tuple{StateEnvsTTN}","page":"StateEnvsTTN","title":"Base.copy","text":"function Base.copy(sysenv::StateEnvsTTN)\n\nShallow copy of StateEnvsTTN.\n\n\n\n\n\n","category":"method"},{"location":"mps/update_site/#Perform-local-updates","page":"Perform local updates","title":"Perform local updates","text":"","category":"section"},{"location":"mps/update_site/","page":"Perform local updates","title":"Perform local updates","text":"At the lowest-level of abstraction, TenNetLib.jl allows for updating the StateEnvs for each sites/bonds manually.","category":"page"},{"location":"mps/update_site/","page":"Perform local updates","title":"Perform local updates","text":"Skip this part if you want to avoid lower-level abstraction.","category":"page"},{"location":"mps/update_site/","page":"Perform local updates","title":"Perform local updates","text":"update_position!(sysenv::StateEnvs, solver, pos::Int, nsite::Int, ortho::String; kwargs...)","category":"page"},{"location":"mps/update_site/#TenNetLib.update_position!-Tuple{StateEnvs, Any, Int64, Int64, String}","page":"Perform local updates","title":"TenNetLib.update_position!","text":"update_position!(sysenv::StateEnvs, solver, pos::Int, nsite::Int, ortho::String; kwargs...)\n\nUpdates StateEnvs at position pos by solver.\n\nArguments:\n\nsysenv::StateEnvs\nsolver: Solver for update. Available ones: eig_solver and exp_solver.\npos::Int: Position of the bond (nsite=2) or site (nsite=1).\nnsite of the environment. Either 1 or 2 for one-site or two-site update respectively.\northo::String: Direction of the sweep. Either \"left\" or \"right\".\n\nNamed arguments and their default values:\n\ntime_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for TDVP. \nnormalize::Bool = true: Whether to normalize after update.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\nnoise::Float64 = 0.0.\nreverse_step::Bool = false if time_step = nothing, true otherwise.\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true.\nsolver_tol::Float64 = 1E-14 if eig_solver, 1E-12 if exp_solver.\nsolver_krylovdim::Int = 5 if eig_solver, 30 if exp_solver.\nsolver_maxiter::Int = 2 if eig_solver, 100 if exp_solver.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false if eig_solver, true if exp_solver.\nsolver_check_convergence::Bool = false if eig_solver, true if exp_solver.\n\nReturn values:\n\n::Float64: Energy.\n::Float64: Truncation Error.\n::Vector{Float64}: SVD spectrum.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#The-TTN-object","page":"The TTN object","title":"The TTN object","text":"","category":"section"},{"location":"ttn/ttn_struct/","page":"The TTN object","title":"The TTN object","text":"TTN\nITensors.siteinds(ttn::TTN)\nITensors.siteind(ttn::TTN, n::Int)\nnumsites(ttn::TTN)\ngetgraph(ttn::TTN)\nBase.getindex(ttn::TTN, node::Int2)\nBase.setindex!(ttn::TTN, tensor::ITensor, node::Int2)\northocenter(ttn::TTN)\nBase.copy(ttn::TTN)\nisvalidnode(ttn::TTN, node::Int2)\nisneighbor(ttn::TTN, node1::Int2, node2::Int2)\nITensors.findsite(ttn::TTN, is)\nITensors.findsites(ttn::TTN, is)\nfindnode(ttn::TTN, is)\nfindnodes(ttn::TTN, is)\nfind_sitenode(ttn::TTN, n::Int)\nfind_sitenodes(ttn::TTN, ns)\nITensors.maxlinkdim(ttn::TTN)\nLinearAlgebra.normalize!(ttn::TTN)","category":"page"},{"location":"ttn/ttn_struct/#TenNetLib.TTN","page":"The TTN object","title":"TenNetLib.TTN","text":"mutable struct TTN{T}\n sites::Vector{Index{T}}\n graph::Graph{Int2}\n tensors::Dict{Int2, ITensor}\n orthocenter::Int2\nend\n\nTree Tensor Network (TTN) object.\n\nEach tensor is indexed by the tuple of integers (::Int2), (ll, nn), where (usually) ll denotes the layer index and nn denotes the tensor index at each layer.\n\nsites::Vector{Index}: Physical site Indexs.\ngraph::Graph{Int2}: Underlying structure of the network defined by Graph{Int2}.\ntensors::Dict{Int2, ITensor}: Tensors in the TTN.\northocenter::Int2: Orthogonality center of the TTN.\n\n\n\n\n\n","category":"type"},{"location":"ttn/ttn_struct/#ITensors.siteinds-Tuple{TTN}","page":"The TTN object","title":"ITensors.siteinds","text":"function ITensors.siteinds(ttn::TTN)\n\nReturns the site Indexs of the TTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#ITensors.siteind-Tuple{TTN, Int64}","page":"The TTN object","title":"ITensors.siteind","text":"function ITensors.siteind(ttn::TTN, n::Int)\n\nReturns the nth site Index of the TTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.numsites-Tuple{TTN}","page":"The TTN object","title":"TenNetLib.numsites","text":"function numsites(ttn::TTN)\n\nReturns the number of physical sites in the TTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.getgraph-Tuple{TTN}","page":"The TTN object","title":"TenNetLib.getgraph","text":"function getgraph(ttn::TTN)\n\nReturns (shallow copy of) the underlying graph of the TTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#Base.getindex-Tuple{TTN, Tuple{Int64, Int64}}","page":"The TTN object","title":"Base.getindex","text":"function Base.getindex(ttn::TTN, node::Int2)\nfunction Base.getindex(ttn::TTN, ll::Int, nn::Int)\n\nReturns the tensor at the node::Int2 = (ll, nn).\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#Base.setindex!-Tuple{TTN, ITensor, Tuple{Int64, Int64}}","page":"The TTN object","title":"Base.setindex!","text":"function Base.setindex!(ttn::TTN, tensor::ITensor, node::Int2)\nfunction Base.setindex!(ttn::TTN, tensor::ITensor, ll::Int, nn::Int)\n\nSets the tensor at the node::Int2 = (ll, nn). If the node is not the orthogonality center, orthogonality center is set to (typemin(Int), typemin(Int)).\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#ITensors.orthocenter-Tuple{TTN}","page":"The TTN object","title":"ITensors.orthocenter","text":"function orthocenter(ttn::TTN)\n\nReturns the orthogonality center of the TTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#Base.copy-Tuple{TTN}","page":"The TTN object","title":"Base.copy","text":"Base.copy(ttn::TTN)\n\nShallow copy of TTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.isvalidnode-Tuple{TTN, Tuple{Int64, Int64}}","page":"The TTN object","title":"TenNetLib.isvalidnode","text":"function isvalidnode(ttn::TTN, node::Int2)\n\nChecks whether the input node::Int2 is a valid node in the TTN graph.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.isneighbor-Tuple{TTN, Tuple{Int64, Int64}, Tuple{Int64, Int64}}","page":"The TTN object","title":"TenNetLib.isneighbor","text":"function isneighbor(ttn::TTN, node1::Int2, node2::Int2)\n\nChecks whether node1 and node2 are neighboring nodes in the TTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#ITensors.findsite-Tuple{TTN, Any}","page":"The TTN object","title":"ITensors.findsite","text":"function ITensors.findsite(ttn::TTN, is)\n\nReturns the first site of the TTN that has at least one Index in common with the Index or ITensor or their collection is.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#ITensors.findsites-Tuple{TTN, Any}","page":"The TTN object","title":"ITensors.findsites","text":"function ITensors.findsites(ttn::TTN, is)\n\nReturns the sites of the TTN that have Indexs in common with the Index or ITensor or their collection is.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.findnode-Tuple{TTN, Any}","page":"The TTN object","title":"TenNetLib.findnode","text":"function findnode(ttn::TTN, is)\n\nReturns the first node of the TTN that has at least one Index in common with the Index or ITensor or their collection is.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.findnodes-Tuple{TTN, Any}","page":"The TTN object","title":"TenNetLib.findnodes","text":"function findnodes(ttn::TTN, is)\n\nReturns the nodes of the TTN that have Indexs in common with the Index or ITensor or their collection is.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.find_sitenode-Tuple{TTN, Int64}","page":"The TTN object","title":"TenNetLib.find_sitenode","text":"function find_sitenode(ttn::TTN, n::Int)\n\nReturn node of the TTN that is associated with the site n. \n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.find_sitenodes-Tuple{TTN, Any}","page":"The TTN object","title":"TenNetLib.find_sitenodes","text":"function find_sitenodes(ttn::TTN, ns)\n\nReturns nodes of the TTN that are associated with the sites ns (a collection of Ints). \n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#ITensors.maxlinkdim-Tuple{TTN}","page":"The TTN object","title":"ITensors.maxlinkdim","text":"function ITensors.maxlinkdim(ttn::TTN)\n\nReturns the maximum bond/link dimension of the TTN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#LinearAlgebra.normalize!-Tuple{TTN}","page":"The TTN object","title":"LinearAlgebra.normalize!","text":"function LinearAlgebra.normalize!(ttn::TTN)\n\nNormalizes the TTN. The TTN must have well-defined orthogonality center.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/","page":"The TTN object","title":"The TTN object","text":"info: Info\nTo conserve global symmetry in TTN, TenNetLib.jl uses a dummy index of dimension one whose flux fixes the superselection sector. This dummy index is attached to one of the tensors of TTN, usually the eccentric central node. Unlike MPS, the fluxes of all tensors in TTN are zero.","category":"page"},{"location":"ttn/ttn_struct/","page":"The TTN object","title":"The TTN object","text":"ITensors.hasqns(ttn::TTN)\nfind_qnnode(ttn::TTN{ITensors.QNBlocks})\nmoveisometry_to_next!(ttn::TTN, node1::Int2, node2::Int2; kwargs...)\nisometrize_full!(ttn::TTN, node::Int2; kwargs...)\nisometrize!(ttn::TTN, node::Int2; kwargs...)","category":"page"},{"location":"ttn/ttn_struct/#ITensors.hasqns-Tuple{TTN}","page":"The TTN object","title":"ITensors.hasqns","text":"function ITensors.hasqns(ttn::TTN)\n\nChecks whether the TTN has QNs.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.find_qnnode-Tuple{TTN{Vector{Pair{QN, Int64}}}}","page":"The TTN object","title":"TenNetLib.find_qnnode","text":"function find_qnnode(ttn::TTN)\n\nReturns the node where the a dummy QN Index is attached to fix the QN sector. Returns nothing if the TTN does not have QN.\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.moveisometry_to_next!-Tuple{TTN, Tuple{Int64, Int64}, Tuple{Int64, Int64}}","page":"The TTN object","title":"TenNetLib.moveisometry_to_next!","text":"function moveisometry_to_next!(ttn::TTN, node1::Int2, node2::Int2; kwargs...)\n\nMoves the isometry / orthogonality center of the TTN from node1::Int2 to the neighboring node2::Int. node1 and node2 must be neighboring nodes. node1 must be the orthogonality center unless ignore_orthocenter = true.\n\nNote: Does not normalize the TTN afterwards.\n\nNamed arguments and their default values.\n\nignore_orthocenter::Bool = false: If set to true, node1 is not required to be the orthogonality center.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.isometrize_full!-Tuple{TTN, Tuple{Int64, Int64}}","page":"The TTN object","title":"TenNetLib.isometrize_full!","text":"function isometrize_full!(ttn::TTN, node::Int2; kwargs...)\n\nIsometrizes the TTN from scratch with respect to the orthogonality center node::Int2.\n\nNamed arguments and their default values.\n\nnormalize::Bool = true: Whether to normalize the TTN afterwards.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\". \n\n\n\n\n\n","category":"method"},{"location":"ttn/ttn_struct/#TenNetLib.isometrize!-Tuple{TTN, Tuple{Int64, Int64}}","page":"The TTN object","title":"TenNetLib.isometrize!","text":"function isometrize!(ttn::TTN, node::Int2; kwargs...)\n\nMoves the isometry / orthogonality center of the TTN to a new center node. If the TTN does not have proper orthoginality center, Isometrizes the TTN from scratch.\n\nNamed arguments and their default values.\n\nnormalize::Bool = true: Whether to normalize the TTN afterwards.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\". \n\n\n\n\n\n","category":"method"},{"location":"mps/sweep/#Sweeping-through-the-MPS","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"","category":"section"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"At a lower level of abstraction, TenNetLib.jl allows to control each fullsweep (left-to-right and right-to-left) manually to update StateEnvs.","category":"page"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"Skip this part if you want to avoid lower-level abstraction.","category":"page"},{"location":"mps/sweep/#SweepData","page":"Sweeping through the MPS","title":"SweepData","text":"","category":"section"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"TenNetLib.jl defines a struct, called SweepData, to store essential data after each fullsweep.","category":"page"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"SweepData\nBase.copy(swdata::SweepData)","category":"page"},{"location":"mps/sweep/#TenNetLib.SweepData","page":"Sweeping through the MPS","title":"TenNetLib.SweepData","text":"mutable struct SweepData\n sweepcount::Int\n maxchi::Vector{Int}\n energy::Vector{Float64}\n entropy::Vector{Float64}\n maxtruncerr::Vector{Float64}\n lasteigs::Vector{Vector{Float64}}\nend\n\nHolds historical data after each (full)sweep. Requires for convergence check etc.\n\nsweepcount::Int: Number of fullsweeps performed.\nmaxchi::Vector{Int}: Maximum MPS bond/link dimensions after every sweep.\nenergy::Vector{Float64}: Energies after every sweep.\nentropy::Vector{Float64}: Mid-chain entropies after every sweep.\nmaxtrucerr::Vector{Float64}: Maximum truncation error after every sweep.\nlasteigs::Vector{Vector{Float64}}: Spectrum of eigenvalues at each bond after previous halfsweep.\n\nDefault constructor:\n\nSweepData(): Initialize an empty SweepData object.\n\n\n\n\n\n","category":"type"},{"location":"mps/sweep/#Base.copy-Tuple{SweepData}","page":"Sweeping through the MPS","title":"Base.copy","text":"Base.copy(swdata::SweepData)\n\nShallow copy of SweepData.\n\n\n\n\n\n","category":"method"},{"location":"mps/sweep/#Perform-a-fullsweep","page":"Sweeping through the MPS","title":"Perform a fullsweep","text":"","category":"section"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"fullsweep!(sysenv::StateEnvs, solver, nsite::Int, swdata::SweepData; kwargs...)","category":"page"},{"location":"mps/sweep/#TenNetLib.fullsweep!-Tuple{StateEnvs, Any, Int64, SweepData}","page":"Sweeping through the MPS","title":"TenNetLib.fullsweep!","text":"function fullsweep!(sysenv::StateEnvs, solver, nsite::Int, swdata::SweepData;\n kwargs...)\n\nPerform a fullsweep (left-to-right and right-to-left) by solver.\n\nArguments:\n\nsysenv::StateEnvs.\nsolver: Solver for update. Available ones: eig_solver and exp_solver.\nnsite::Int of the environment. Either 1 or 2 for one-site or two-site update respectively.\nswdata::SweepData.\n\nNamed arguments and their default values:\n\ntime_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for TDVP. \nnormalize::Bool = true: Whether to normalize after update.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\nnoise::Float64 = 0.0.\nreverse_step::Bool = false if time_step = nothing, true otherwise.\noutputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true.\nsolver_tol::Float64 = 1E-14 if eig_solver, 1E-12 if exp_solver.\nsolver_krylovdim::Int = 5 if eig_solver, 30 if exp_solver.\nsolver_maxiter::Int = 2 if eig_solver, 100 if exp_solver.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false if eig_solver, true if exp_solver.\nsolver_check_convergence::Bool = false if eig_solver, true if exp_solver.\n\nReturn values:\n\n::Float64: Change in Energy ΔE\n::Float64: Change in Entropy ΔS\n\nswdata::SweepData gets updated.\n\n\n\n\n\n","category":"method"},{"location":"mps/sweep/#Perform-a-dynamical-fullsweep","page":"Sweeping through the MPS","title":"Perform a dynamical fullsweep","text":"","category":"section"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"TenNetLib.jl defines the following function to dynamically decide whether to perform single- or two-site update at each bond, depending on the entropy growth at the previous halfsweep.","category":"page"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"dynamic_fullsweep!(sysenv::StateEnvs, solver, swdata::SweepData; kwargs...)","category":"page"},{"location":"mps/sweep/#TenNetLib.dynamic_fullsweep!-Tuple{StateEnvs, Any, SweepData}","page":"Sweeping through the MPS","title":"TenNetLib.dynamic_fullsweep!","text":"function dynamic_fullsweep!(sysenv::StateEnvs, solver, swdata::SweepData;\n kwargs...)\n\nPerform a dynamic fullsweep (left-to-right and right-to-left) by solver. The very first sweep, as dictated by swdata.sweepcount=0, Global Subspace Expansion (see below) is performed followed by a pure one-site sweep if typeof(sysenv) == StateEnvs{ProjMPO}, else performs a full two-site sweep. At each bond, if the lowest eigenvalue is below eigthreshold or the bond dimension at that bond has reached maxdim at a particular halfsweep, performs single-site update across that bond in the subsequent halfsweep, otherwise performs two-site update.\n\nArguments:\n\nsysenv::StateEnvs.\nsolver: Solver for update. Available ones: eig_solver and exp_solver.\nswdata::SweepData.\n\nNamed arguments and their default values:\n\ntime_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for TDVP. \nnormalize::Bool = true: Whether to normalize after update.\nmaxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.\nmindim::Int = 1: Minimum bond dimension after SVD truncation.\ncutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.\nsvd_alg::String = \"divide_and_conquer\".\nnoise::Float64 = 0.0.\nreverse_step::Bool = false if time_step = nothing, true otherwise.\noutputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.\neigthreshold::Float64 = 1E-12.\nextendat::Union{Nothing, Int} = nothing: If specified, at every extendatth sweep, Global Subspace Expansion is performed followed by a pure one-site sweep if typeof(sysenv) == StateEnvs{ProjMPO}, else performs a full two-site sweep.\n\nNamed arguments for solver and their default values:\n\nSee the documentation of KrylovKit.jl.\n\nishermitian::Bool = true.\nsolver_tol::Float64 = 1E-14 if eig_solver, 1E-12 if exp_solver.\nsolver_krylovdim::Int = 3 if eig_solver, 30 if exp_solver.\nsolver_maxiter::Int = 1 if eig_solver, 100 if exp_solver.\nsolver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.\nsolver_eager::Bool = false if eig_solver, true if exp_solver.\nsolver_check_convergence::Bool = false if eig_solver, true if exp_solver.\n\nArguments for Global Subspace Expansion and their default values:\n\nextension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.\nextension_applyH_cutoff::Float64 = 0.0: Cutoff for the application of the MPO to the MPS.\nextension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension for the application of the MPO to the MPS.\nextension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.\n\nReturn values:\n\n::Float64: Change in Energy ΔE\n::Float64: Change in Entropy ΔS\n\nswdata::SweepData gets updated.\n\n\n\n\n\n","category":"method"},{"location":"mps/sweep/#Global-Subspace-Expansion","page":"Sweeping through the MPS","title":"Global Subspace Expansion","text":"","category":"section"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"Following Phys. Rev. B 102, 094315 (2020), a Global Subspace Expansion can be performed using Krylov subspace if the environments are created by a single MPO.","category":"page"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"krylov_extend!(psi::MPS, H::MPO; kwargs...)\nkrylov_extend!(sysenv::StateEnvs{ProjMPO}; kwargs...)","category":"page"},{"location":"mps/sweep/#TenNetLib.krylov_extend!-Tuple{MPS, MPO}","page":"Sweeping through the MPS","title":"TenNetLib.krylov_extend!","text":"function krylov_extend!(psi::MPS, H::MPO; kwargs...)\n\nPerforms Global Subspace Expansion.\n\nArguments and their default values:\n\nextension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.\nextension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.\nextension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.\nextension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.\n\n\n\n\n\n","category":"method"},{"location":"mps/sweep/#TenNetLib.krylov_extend!-Tuple{StateEnvs{ProjMPO}}","page":"Sweeping through the MPS","title":"TenNetLib.krylov_extend!","text":"function krylov_extend!(sysenv::StateEnvs{ProjMPO}; kwargs...)\n\nPerforms Global Subspace Expansion. The StateEnvs must be created by a single MPO.\n\nArguments and their default values:\n\nextension_krylovdim::Int = 3: Number of Krylov vectors used for GSE.\nextension_applyH_cutoff::Float64 = Float64_threshold(): Cutoff for the application the MPO to the MPS.\nextension_applyH_maxdim::Int = maxlinkdim(psi) + 1: Maximum bond/link dimension of the resulting MPS after the application of the MPO to the MPS.\nextension_cutoff::Float64 = 1E-10: Cutoff for the basis extension step in GSE.\n\n\n\n\n\n","category":"method"},{"location":"mps/sweep/","page":"Sweeping through the MPS","title":"Sweeping through the MPS","text":"info: Info\nApart from TDVP, Global Subspace Expansion is also very useful for DMRG to get rid of nasty local minimas.","category":"page"},{"location":"ttn/measure_ttn/#Measuring-the-TTN","page":"Measuring the TTN","title":"Measuring the TTN","text":"","category":"section"},{"location":"ttn/measure_ttn/","page":"Measuring the TTN","title":"Measuring the TTN","text":"measure(::Type{T}, psi::TTN, opten::ITensor) where T <: Union{ComplexF64, Float64}\nmeasure(::Type{T}, psi::TTN, opstr::String, pos::Int) where T <: Union{ComplexF64, Float64}\nmeasure(::Type{T}, psi::TTN, opstr::String; kwargs...) where T <: Union{ComplexF64, Float64}\nmeasure(::Type{T}, psi::TTN, optens::Vector{ITensor}) where T <: Union{ComplexF64, Float64}\nmeasure(::Type{T}, psi::TTN, oppairs::Vector{Pair{String, Int}}; isfermions::Bool = true) where T <: Union{ComplexF64, Float64}","category":"page"},{"location":"ttn/measure_ttn/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, TTN, ITensor}} where T<:Union{Float64, ComplexF64}","page":"Measuring the TTN","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::TTN, opten::ITensor)\n\nReturns (complex / real) local expectation value (::ComplexF64 / ::Float64) of a given TTN psi::TTN. The operator opten::ITensor must be single-site operator.\n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\n\n\n\n\n","category":"method"},{"location":"ttn/measure_ttn/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, TTN, String, Int64}} where T<:Union{Float64, ComplexF64}","page":"Measuring the TTN","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::TTN, opstr::String, pos::Int)\n\nReturns (complex / real) local expectation value (::ComplexF64 / ::Float64) of a given TTN psi::TTN for a given operator name (opstr::String) and a site index (pos::Int) \n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\n\n\n\n\n","category":"method"},{"location":"ttn/measure_ttn/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, TTN, String}} where T<:Union{Float64, ComplexF64}","page":"Measuring the TTN","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::TTN, opstr::String; kwargs...)\n\nReturns (complex / real) local expectation values (::Vector{ComplexF64} / ::Vector{Float64}) of a given TTN psi::TTN for a given operator name (opstr::String) at all the sites.\n\nOptionally, for specific sites, keyword argument sites can be specified, e.g., sites = [1, 2, 3].\n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\n\n\n\n\n","category":"method"},{"location":"ttn/measure_ttn/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, TTN, Vector{ITensor}}} where T<:Union{Float64, ComplexF64}","page":"Measuring the TTN","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::TTN, optens::Vector{ITensor})\n\nReturns (complex / real) multi-site expectation value (::ComplexF64 / ::Float64) of a given TTN psi::TTN for a given vector of single-site operators (optens::Vector{ITensor}).\n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\n\n\n\n\n","category":"method"},{"location":"ttn/measure_ttn/#TenNetLib.measure-Union{Tuple{T}, Tuple{Type{T}, TTN, Vector{Pair{String, Int64}}}} where T<:Union{Float64, ComplexF64}","page":"Measuring the TTN","title":"TenNetLib.measure","text":"function measure(::Type{ElT} = ComplexF64, psi::TTN, oppairs::Vector{Pair{String, Int}};\n isfermions::Bool = true)\n\nReturns (complex / real) multi-site expectation value (::ComplexF64 / ::Float64) of a given TTN psi::TTN. oppairs::Vector{Pair{String, Int}} contains pairs of operator names (String) and site locations (Int). E.g., for <ψ|OᵢOⱼOₖ... |ψ>, oppairs = [\"O\" => i, \"O\" => j, \"O\" => k,...].\n\nFermionic JW strings are added automatically for fermionic operators if isfermions::Bool = true (default).\n\nFor ElT = Float64, if the expectation value is complex, raises a warning!\n\nExample:\n\nvalueC = measure(psi, [\"Cdag\" => 2, \"C\" => 6, \"Cdag\" => 9, \"C\" => 12])\nvalueR = measure(Float64, psi, [\"Cdag\" => 2, \"C\" => 6, \"Cdag\" => 9, \"C\" => 12])\n\n\n\n\n\n","category":"method"},{"location":"base/fermions/#Dealing-with-Fermions","page":"Dealing with Fermions","title":"Dealing with Fermions","text":"","category":"section"},{"location":"base/fermions/","page":"Dealing with Fermions","title":"Dealing with Fermions","text":"TenNetLib.jl uses the following function to teat fermionic operators.","category":"page"},{"location":"base/fermions/","page":"Dealing with Fermions","title":"Dealing with Fermions","text":"bosonize(oppair::Vector{Pair{String, Int}},sites::Vector{Index{T}}) where T","category":"page"},{"location":"base/fermions/#TenNetLib.bosonize-Union{Tuple{T}, Tuple{Vector{Pair{String, Int64}}, Array{Index{T}, 1}}} where T","page":"Dealing with Fermions","title":"TenNetLib.bosonize","text":"function bosonize(oppair::Vector{Pair{String, Int}},\n sites::Vector{Index{T}}) where T\n\nGiven a string of operator names with positions in the form of Vector{Pair{String, Int}} \"bosonizes\" the operator string by putting the Jordan-Wigner string \"F\" at appropriate places.\n\nArguments\n\noppair::Vector{Pair{String, Int}}: Input string of operator names with positions.\nsites::Vector{Index}: The entire site Indexs as per ITensors' convention.\n\nReturn values\n\n::Int: Even (+1) or odd (-1) permutation.\n::Vector{Pair{String, Int}}: modified string of operator names and positions.\n\n\n\n\n\n","category":"method"},{"location":"#TenNetLib.jl","page":"Introduction","title":"TenNetLib.jl","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"A Tensor Network Library (TenNetLib.jl) built on top of ITensors.jl for quantum many-body problems.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"Build Status Documentation\n(Image: Build Status) (Image: Build Status)","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"The source code for TenNetLib.jl can be found on GitHub","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"The documentation for TenNetLib.jl can be found here.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"This library requires Julia 1.7+.","category":"page"},{"location":"#Overview","page":"Introduction","title":"Overview","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"TenNetLib.jl features widely-used Tensor Network (TN) codes, designed with a multi-layered abstraction to cater to diverse user needs. The library provides users with varying levels of control over their computations. Currently, TenNetLib.jl presents an array of functionalities for:","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"(a) Finite-size Matrix-Product States (MPS): Different variants of Density Matrix Renormalization Group (DMRG) and Time Dependent Variational Principle (TDVP) (including subspace expansion) methods.\n(b) Tree Tensor Network (TTN): Variational search for the ground state and first few excited states.","category":"page"},{"location":"#Installation","page":"Introduction","title":"Installation","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"TenNetLib.jl is registered on Julia General Registry. To install the library (along with ITensors.jl), you can use the following steps:","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"$ julia\n\njulia> ]\n\npkg> add ITensors\n\npkg> add TenNetLib","category":"page"},{"location":"#Found-an-issue-or-bug?","page":"Introduction","title":"Found an issue or bug?","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"\"Beware of bugs in the above code; I have only proved it correct, not tried it.\" – Donald Knuth","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"If you find bugs or a mistakes of any kind, please let us know by adding an issue to the GitHub issue tracker. You are also welcome to submit a pull request.","category":"page"},{"location":"#Future-functionality?","page":"Introduction","title":"Future functionality?","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"Here is a list for future additions in the decreasing order of priority. Any help / suggestion is welcome.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"Augmented Tree Tensor Network (aTTN) for variational ground state search for 2D problems.\nInfinite DMRG (iDMRG) and/or Variational Uniform Matrix Product States (VUMPS) to tackle 1D / quasi-1D problems directly at the thermodynamic limit.\nProjected Entangled Pair States (PEPS) for 2D problems.\nReal-time evolution method using PEPS and TTN.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"Also, please feel free to ask about a new feature by adding a new request to the GitHub issue tracker labelled feature request. Note that submitting a pull request, providing the needed changes to introduced your requested feature, will speed up the process.","category":"page"},{"location":"#Example:-A-simple-DMRG-code","page":"Introduction","title":"Example: A simple DMRG code","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The following code is for a simple DMRG run at the highest level of abstraction without any additional control.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"using ITensors\nusing TenNetLib\n\nlet\n N = 32\n sites = siteinds(\"S=1/2\",N)\n os = OpSum()\n \n for j=1:N-1\n os += 1, \"Sz\", j,\"Sz\", j+1\n os += 0.5, \"S+\", j, \"S-\", j+1\n os += 0.5, \"S-\", j, \"S+\", j+1\n end\n \n H = MPO(os,sites)\n states = [isodd(n) ? \"Up\" : \"Dn\" for n in 1:N]\n psi0 = MPS(sites, states)\n\n params = DMRGParams(;nsweeps = [5, 5], maxdim = [20, 50],\n cutoff = 1e-14, noise = 1e-3, noisedecay = 2,\n disable_noise_after = 3)\n\n # dmrg2 for two-site DMRG\n en, psi = dmrg2(psi0, H, params)\nend","category":"page"},{"location":"#Example:-A-simple-TDVP-code","page":"Introduction","title":"Example: A simple TDVP code","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The following code is for a simple TDVP run at the highest level of abstraction without any additional control.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"using ITensors\nusing TenNetLib\n\nlet\n N = 32\n sites = siteinds(\"S=1/2\",N)\n os = OpSum()\n \n for j=1:N-1\n os += 1, \"Sz\", j,\"Sz\", j+1\n os += 0.5, \"S+\", j, \"S-\", j+1\n os += 0.5, \"S-\", j, \"S+\", j+1\n end\n \n H = MPO(os,sites)\n states = [isodd(n) ? \"Up\" : \"Dn\" for n in 1:N]\n psi0 = MPS(sites, states)\n\n tau = -0.01im \n engine = TDVPEngine(psi0, H)\n for ii = 1:100\n\n \t# `nsite = \"dynamic\"` for dynamical selection between\n\t# single- and two-site variants at different bonds\n tdvpsweep!(engine, tau,\n nsite = \"dynamic\";\n maxdim = 200,\n cutoff = 1E-12,\n extendat = 5)\n\n\tpsi = getpsi(engine)\n\t# DO STUFF\n end\nend","category":"page"},{"location":"#Example:-A-simple-TTN-ground-state-optimzation-code","page":"Introduction","title":"Example: A simple TTN ground-state optimzation code","text":"","category":"section"},{"location":"","page":"Introduction","title":"Introduction","text":"The following code is for a simple TTN ground-state optimzation run at the highest level of abstraction without any additional control. Here we use OpStrings and CouplingModel instead of OpSum and MPO.","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"using ITensors\nusing TenNetLib\n\nlet\n N = 32\n sites = siteinds(\"S=1/2\",N)\n os = OpStrings()\n \n for j=1:N-1\n os += 1, \"Sz\" => j,\"Sz\" => j+1\n os += 0.5, \"S+\" => j, \"S-\" => j+1\n os += 0.5, \"S-\"=> j, \"S+\" => j+1\n end\n \n H = CouplingModel(os,sites)\n psi0 = TTN(sites, 64, QN(\"Sz\", 0))\n\n sweeppath = default_sweeppath(psi0)\n \n params = OptimizeParamsTTN(; maxdim = [64, 128], nsweeps = [5, 10], \n cutoff = 1e-14, noise = 1e-2, noisedecay = 5, \n disable_noise_after = 5)\n\t\t\t \n en, psi = optimize(psi0, H, params, sweeppath)\nend","category":"page"},{"location":"","page":"Introduction","title":"Introduction","text":"","category":"page"}] +} diff --git a/v0.1.0/siteinfo.js b/v0.1.0/siteinfo.js new file mode 100644 index 0000000..a7a85ce --- /dev/null +++ b/v0.1.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.1.0"; diff --git a/v0.1.0/ttn/TTN.png b/v0.1.0/ttn/TTN.png new file mode 100644 index 0000000..1adbd8a Binary files /dev/null and b/v0.1.0/ttn/TTN.png differ diff --git a/v0.1.0/ttn/example_optimize/index.html b/v0.1.0/ttn/example_optimize/index.html new file mode 100644 index 0000000..6e5d3ce --- /dev/null +++ b/v0.1.0/ttn/example_optimize/index.html @@ -0,0 +1,56 @@ + +Example: Optimizing TTN · TenNetLib.jl

Example: Optimizing TTN

A straight-forward TTN optimization can be performed as follows.

using ITensors
+using TenNetLib
+
+let
+    N = 32
+    sites = siteinds("S=1/2",N)
+    os = OpStrings()
+    
+    for j=1:N-1
+        os += 1, "Sz" => j, "Sz" => j+1
+        os += 0.5, "S+" => j, "S-" => j+1
+        os += 0.5, "S-" => j, "S+" => j+1
+    end
+    
+    H = CouplingModel(os,sites)
+
+    psi0 = default_randomTTN(sites, 12, QN("Sz", 0))
+    sweeppath = default_sweeppath(psi0)
+
+    params = OptimizeParamsTTN(; nsweeps = [10, 10], maxdim = [20, 50],
+                               cutoff = 1e-14, noise = 1e-3, noisedecay = 2,
+                               disable_noise_after = 5)
+
+    en, psi = optimize(psi0, H, params, sweeppath)
+end
Warning

For TTN optimzaion, direct MPO input is not supported. One can, however, prepare a CouplingModel from MPO using CouplingModel(mpos::MPO...).

Instead of using such higher-level code, one can also use lower-level functions for a better control.

sysenv = StateEnvsTTN(psi0, H)
+
+swdata = optimize!(sysenv, params, sweeppath)
+
+# Get energy from `Sweepdata`
+energy = swdata.energy[end]
+
+# take a shallow copy of the TTN
+# if the `StateEnvsTTN` will be updated later again
+psi = getpsi(sysenv)
+
+# Alternatively, take the psi from `StateEnvsTTN` itself.
+# NOTE: This can crash the simulation, if the TTN is modified (e.g., in measurements)
+# and `StateEnvsTTN` is going to be updated later on.
+# psi = sysenv.psi

Excited state search is also straightforword.

# Given a ground state `psi_gr`, initial TTN `psi0`,
+# and a Hamiltonian `H`
+
+en, psi = optimize(psi0, H, [psi_gr], params, sweeppath; weight = 10.0)

Similarly, using StateEnvsTTN:

sysenv_ex = StateEnvsTTN(psi0, H, [psi_gr]; weight = 10.0)
+swdata_ex = optimize!(sysenv_ex, params, sweeppath)
+
+# Get energy from `Sweepdata`
+energy1 = swdata_ex.energy[end]
+
+# take a shallow copy of the TTN
+# if the `StateEnvsTTN` will be updated later again
+psi1 = getpsi(sysenv_ex)
+
+# Alternatively, take the psi from `StateEnvsTTN` itself.
+# NOTE: This can crash the simulation, if the TTN is modified (e.g., in measurements)
+# and `StateEnvsTTN` is going to be updated later.
+# psi1 = sysenv_ex.psi
diff --git a/v0.1.0/ttn/measure_ttn/index.html b/v0.1.0/ttn/measure_ttn/index.html new file mode 100644 index 0000000..66b9bb5 --- /dev/null +++ b/v0.1.0/ttn/measure_ttn/index.html @@ -0,0 +1,4 @@ + +Measuring the TTN · TenNetLib.jl

Measuring the TTN

TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::TTN, opten::ITensor)

Returns (complex / real) local expectation value (::ComplexF64 / ::Float64) of a given TTN psi::TTN. The operator opten::ITensor must be single-site operator.

For ElT = Float64, if the expectation value is complex, raises a warning!

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::TTN, opstr::String, pos::Int)

Returns (complex / real) local expectation value (::ComplexF64 / ::Float64) of a given TTN psi::TTN for a given operator name (opstr::String) and a site index (pos::Int)

For ElT = Float64, if the expectation value is complex, raises a warning!

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::TTN, opstr::String; kwargs...)

Returns (complex / real) local expectation values (::Vector{ComplexF64} / ::Vector{Float64}) of a given TTN psi::TTN for a given operator name (opstr::String) at all the sites.

Optionally, for specific sites, keyword argument sites can be specified, e.g., sites = [1, 2, 3].

For ElT = Float64, if the expectation value is complex, raises a warning!

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::TTN, optens::Vector{ITensor})

Returns (complex / real) multi-site expectation value (::ComplexF64 / ::Float64) of a given TTN psi::TTN for a given vector of single-site operators (optens::Vector{ITensor}).

For ElT = Float64, if the expectation value is complex, raises a warning!

source
TenNetLib.measureMethod
function measure(::Type{ElT} = ComplexF64, psi::TTN, oppairs::Vector{Pair{String, Int}};
+                 isfermions::Bool = true)

Returns (complex / real) multi-site expectation value (::ComplexF64 / ::Float64) of a given TTN psi::TTN. oppairs::Vector{Pair{String, Int}} contains pairs of operator names (String) and site locations (Int). E.g., for <ψ|OᵢOⱼOₖ... |ψ>, oppairs = ["O" => i, "O" => j, "O" => k,...].

Fermionic JW strings are added automatically for fermionic operators if isfermions::Bool = true (default).

For ElT = Float64, if the expectation value is complex, raises a warning!

Example:

valueC = measure(psi, ["Cdag" => 2, "C" => 6, "Cdag" => 9, "C" => 12])
+valueR = measure(Float64, psi, ["Cdag" => 2, "C" => 6, "Cdag" => 9, "C" => 12])
source
diff --git a/v0.1.0/ttn/optimize_ttn/index.html b/v0.1.0/ttn/optimize_ttn/index.html new file mode 100644 index 0000000..cd1114b --- /dev/null +++ b/v0.1.0/ttn/optimize_ttn/index.html @@ -0,0 +1,24 @@ + +Optimizing TTN · TenNetLib.jl

Optimizing TTN

Functions to optimize TTN.

OptimizeParamsTTN

TenNetLib.jl defines a struct, called OptimizeParamsTTN, to control TTN optimizations.

TenNetLib.OptimizeParamsTTNType
mutable struct OptimizeParamsTTN
+    maxdim::Vector{Int}
+    nsweeps::Vector{Int}
+    cutoff::Vector{Float64}
+    noise::Vector{Float64}
+    noisedecay::Vector{Float64}
+    disable_noise_after::Vector{Int}
+end

Holds parameters to control the optimzation sweeps of the TTN.

  • maxdim::Vector{Int}: Maximum allowed TTN bond/link dimensions at each stages of optimization.
  • nsweeps::Vector{Int}: Number of sweeps to be performed at each statges of optimization.
  • cutoff::Vector{Float64}: Cutoff for SVD truncation at each stages of optimization.
  • noise::Vector{Float64}: Noise level at each stages of optimization.
  • noisedecay::Vector{Float64}: Decay of noise level at each states of optimization.

Noise is divided by noisedecay after each sweep.

  • disable_noise_after::Vector{Int}: Switch of noise after this many sweeps at each

states of optimization.

All these Vectors must have same dimension.

source
TenNetLib.OptimizeParamsTTNMethod
function OptimizeParamsTTN(;maxdim::Vector{Int}, nsweeps::Vector{Int}, 
+                           cutoff::Union{Vector{Float64}, Float64} = Float64_threshold(),
+                           noise::Union{Vector{Float64}, Float64, Int} = 0.0,
+                           noisedecay::Union{Vector{Float64}, Float64, Int} = 1.0,
+                           disable_noise_after::Union{Vector{Int}, Int} = typemax(Int))

Constructor for OptimizeParamsTTN. Takes named arguments.

  • maxdim::Vector{Int}: Maximum allowed TTN bond/link dimensions at each stages of optimization.
  • nsweeps::Vector{Int}: Number of sweeps to be performed at each statges of optimization.
  • cutoff::Union{Float64, Vector{Float64}} = Float64_threshold(): Cutoff for SVD truncation at each stages of optimization. If Float64, cutoff remains same throughout the optimization simulation.
  • noise::Union{Float64, Int, Vector{Float64}} = 0.0: Noise level at each stages of optimization. If Float64 / Int, initial noise remains same throughout the optimization.
  • noisedecay::Union{Float64, Int, Vector{Float64}} = 1.0: Decay of noise level at each states of optimization. Noise is divided by noisedecay after each sweep. If Float64 / Int, noisedecay remains same throughout the DMRG simulation.
  • disable_noise_after::Union{Int, Vector{Int}} = typemax(Int): Switch of noise after this many sweeps at each states of optimization. If Int, disable_noise_after remains same throughout the optimization.
source
Base.copyMethod
Base.copy(params::OptimizeParamsTTN)

Shallow copy OptimizeParamsTTN.

source

A lower level optimization function

Following function modifies StateEnvsTTN in-place. Skip this function if you want to avoid lower-level abstraction.

TenNetLib.optimize!Method
function optimize!(sysenv::StateEnvsTTN,
+                   params::OptimizeParamsTTN,
+                   sweeppath::Vector{Int2};
+                   kwargs...)

Performs optimization of the TTN.

Arguments:

  • sysenv::StateEnvsTTN.
  • params::OptimizationParamsTTN.
  • sweeppath::Vector{Int2}: The path to be followed during optimization sweep. A vector that must contain all the nodes atleast once.

Named arguments and their default values:

  • normalize::Bool = true: Whether to normalize after update.
  • svd_alg::String = "divide_and_conquer".
  • weight::Float64 = -1.0: Weight for the excited state calculation. Must be set to greater than 0 for the excited state optimization.
  • outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Convergence criteria:

  • energyErrGoal: Optimization (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and the optimzation moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.

Named arguments for eig_solver and their default values:

See documentation of KrylovKit.jl.

  • ishermitian::Bool = true
  • solver_tol::Float64 = 1E-14.
  • solver_krylovdim::Int = 3.
  • solver_maxiter::Int = 1.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false.
  • solver_check_convergence::Bool = false.

Return values:

  • SweepDataTTN
source

Higher level optimzation functions

TenNetLib.optimizeMethod
function optimize(psi0::TTN, H::CouplingModel,
+                  params::OptimizeParamsTTN,
+                  sweeppath::Vector{Int2};
+                  kwargs...)
+
+function optimize(psi0::TTN, H::CouplingModel, Ms::Vector{TTN},
+                  params::OptimizeParamsTTN,
+                  sweeppath::Vector{Int2};
+                  kwargs...)

Performs optimization of the TTN.

Arguments:

  • psi0::TTN: Initial TTN.
  • H::CouplingModel, Ms::Vector{MPS}.
  • params::OptimizationParamsTTN.
  • sweeppath::Vector{Int2}: The path to be followed during optimization sweep. A vector that must contain all the nodes atleast once.

Named arguments and their default values:

  • normalize::Bool = true: Whether to normalize after update.
  • svd_alg::String = "divide_and_conquer".
  • weight::Float64 = -1.0: Weight for the excited state calculation. Must be set to greater than 0 for the excited state optimization.
  • outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Convergence criteria:

  • energyErrGoal: Optimization (at a particluar stage) stops when energy difference between two consecutive sweeps falls below this threshold and the optimzation moves to the next stage. noise must be below Float64_threshold() to trigger this early stopping.

Named arguments for eig_solver and their default values:

See documentation of KrylovKit.jl.

  • ishermitian::Bool = true
  • solver_tol::Float64 = 1E-14.
  • solver_krylovdim::Int = 3.
  • solver_maxiter::Int = 1.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false.
  • solver_check_convergence::Bool = false.

Return values:

  • ::Float64: Energy.
  • ::TTN: The state psi.
source
diff --git a/v0.1.0/ttn/state_envs_ttn/index.html b/v0.1.0/ttn/state_envs_ttn/index.html new file mode 100644 index 0000000..575e92f --- /dev/null +++ b/v0.1.0/ttn/state_envs_ttn/index.html @@ -0,0 +1,11 @@ + +StateEnvsTTN · TenNetLib.jl

StateEnvsTTN: A container to store the TTN and its environments

Similar to the setup for MPS, tt the lowest-level of abstraction, TenNetLib.jl defines StateEnvs to hold a TTN and its environments to be modified in place.

Skip this part if you want to avoid lower-level abstraction.

TenNetLib.StateEnvsTTNType
mutable struct StateEnvsTTN{T1, T2 <: Union{EnvCouplingModelTTN,
+                                            EnvCouplingModelProjTTN}}
+    psi::TTN{T1}
+    env::T{T2}
+end

Holds the TTN and the environment.

source
TenNetLib.StateEnvsTTNMethod
function StateEnvsTTN(psi::TTN, H::CouplingModel)

Constructor of the StateEnvsTTN from a CouplingModel. Each terms in the CouplingModel are contracted in parallel.

source
TenNetLib.StateEnvsTTNMethod
function StateEnvsTTN(psi::TTN, H::CouplingModel, Ms::Vector{TTN}; weight::Float64)

Constructor of StateEnvsTTN from a CouplingModel and a vector of TTN used for excited state search. Each terms in the CouplingModel are contracted in parallel.

source
TenNetLib.getpsiMethod
function getpsi(sysenv::StateEnvsTTN)

Returns (shallow copy of) the state psi.

source
TenNetLib.getenvMethod
function getenv(sysenv::StateEnvsTTN)

Returns (shallow copy of) the environment env.

source
ITensors.position!Method
function position!(sysenv::StateEnvsTTN, node::Int2;
+                   maxdim::Int = typemax(Int),
+                   mindim::Int = 1,
+                   cutoff::Float64 = _Float64_Threshold,
+                   svd_alg::String = "divide_and_conquer",
+                   normalize::Bool = true)

Moves the orthogonality center of the TTN to node and updates the effective Hamiltonian of the same.

Named arguments and their default values:

  • normalize::Bool = true: Whether to normalize afterwards.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
source
TenNetLib.productMethod
function product(sysenv::StateEnvsTTN, v::ITensor)

Returns the Matrix-Vector product between the environment and input ITensor v.

source
Base.copyMethod
function Base.copy(sysenv::StateEnvsTTN)

Shallow copy of StateEnvsTTN.

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diff --git a/v0.1.0/ttn/sweep_ttn/index.html b/v0.1.0/ttn/sweep_ttn/index.html new file mode 100644 index 0000000..9bb3867 --- /dev/null +++ b/v0.1.0/ttn/sweep_ttn/index.html @@ -0,0 +1,7 @@ + +Sweeping through the TTN · TenNetLib.jl

Sweeping through the TTN

At a lower level of abstraction, TenNetLib.jl allows to control each fullsweep manually to update StateEnvsTTN.

Skip this part if you want to avoid lower-level abstraction.

SweepDataTTN

TenNetLib.jl defines a struct, called SweepDataTTN, to store essential data after each fullsweep.

TenNetLib.SweepDataTTNType
mutable struct SweepDataTTN
+    sweepcount::Int
+    maxchi::Vector{Int}
+    energy::Vector{Float64}
+end

Holds historical data after each (full)sweep of the TTN. Requires for convergence check etc.

  • sweepcount::Int: Number of fullsweeps performed.
  • maxchi::Vector{Int}: Maximum MPS bond/link dimensions after every sweep.
  • energy::Vector{Float64}: Energies after every sweep.

Default constructor:

  • SweepDataTTN(): Initialize an empty SweepData object.
source
Base.copyMethod
Base.copy(swdata::SweepDataTTN)

Shallow copy of SweepDataTTN.

source

sweeppath

TenNetLib.default_sweeppathFunction
function default_sweeppath(psi::TTN)

For a given a TTN having the default hierarchical binary tree structure, teturns the default path for sweeping through the TTN.

Return values:

  • Vector{Int2}: The list of nodes as the path to be followed during a (half)sweep.
source

Perform a fullsweep

TenNetLib.fullsweep!Method
function fullsweep!(sysenv::StateEnvsTTN, sweeppath::Vector{Int2}, solver,
+                    swdata::SweepDataTTN; kwargs...)

Perform a fullsweep of the TTN by solver.

Arguments:

  • sysenv::StateEnvsTTN.
  • sweeppath::Vector{Int2}: The list of nodes as the path to be followed during a (half)sweep. Must have each node atleast once. For the next halfsweep the reverse path is followed.
  • solver: Solver for update. Currently only eig_solver is supported.
  • swdata::SweepDataTTN.

Named arguments and their default values:

  • time_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for future functionality.
  • normalize::Bool = true: Whether to normalize after update.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
  • noise::Float64 = 0.0.
  • expand_dim::Int = 0 if noise == 0 else 20. Dimension to be expanded (on top of maxdim) during subspace expansion.
  • max_expand_dim::Int = 2 * expand_dim. maximum dimension to be expanded during subspace expansion.
  • expand_numiter::Int = 4. Number of iteration for subspace expansion. Should be greater than 1.
  • linkwise_maxdim::Union{Nothing, Dict{LinkTypeTTN, Int}} = nothing. Specifies maximum bond dimension of a particular link.
  • outputlevel::Int = 1. If 0 prints no information, for 1 outputs after every fullsweep, if 2 prints at every update step.

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true.
  • solver_tol::Float64 = 1E-14.
  • solver_krylovdim::Int = 5.
  • solver_maxiter::Int = 2.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false.
  • solver_check_convergence::Bool = false.

Return values:

  • ::Float64: Change in Energy ΔE

swdata::SweepDataTTN gets updated.

source
diff --git a/v0.1.0/ttn/ttn/index.html b/v0.1.0/ttn/ttn/index.html new file mode 100644 index 0000000..c4d3b3a --- /dev/null +++ b/v0.1.0/ttn/ttn/index.html @@ -0,0 +1,5 @@ + +Tree Tensor Networks · TenNetLib.jl

Tree Tensor Networks (TTN)

Tree Tensor Network (TTN) is a loop-free hierarchical tensor network (see belew).

Tree Tensor Network for a system of size 16
Tree Tensor Network

Due to enhanced connectivity in the structure of TTN, it can support long-range quantum correlations comapred to MPS. Moreover, simulations for systems with periodic boundary conditions (PBC) are almost as efficient as the same with open boundary conditions (OBC). TTNs have found their place for simulating 2D or pseudo-2D ladder/cylinder systems with PBC where the performance of MPS is not adequate.

TenNetLib.jl implements the unconstrained optimization for obtaining ground as well as excited states as described in Phys. Rev. B 90, 125154 (2014) and SciPost Phys. Lect. Notes 8 (2019).


Each tensor in the TTN are indexed by a pair (Tuple) of Ints = (ll, nn).

In the default scenario, ll denotes the layer index and nn denotes the tensor index at each layer (see the image above). The counting for ll, in the default case, starts at the bottom (towards to top level), while nn counts from left. The structure of the network is defined by a Graph{Int2} object. The link / bond between two neighboring nodes is denoted by a LinkTypeTTN object, an unordered pair of Int2s.

TenNetLib.LinkTypeTTNType
struct LinkTypeTTN
+    first::Int2
+    second::Int2
+end

Link / bond between two nodes first and second.

source
Info

The order of the nodes inside LinkTypeTTN is irrelevant, i.e., LinkTypeTTN(node1, node2) == LinkTypeTTN(node2, node1).


Info

TenNetLib.jl can automatically handle system-sizes that are not powers of 2. No special care is needed for such system-sizes.

TTN for system-size 12TTN for system-size 14
Sites 1, 4, 7, 11 are directly connected to ll=2 tensorsSites 5, 12 are directly connected to ll=2 tensors
Nodes (1,1), (1,3), (1,5), (1,7) are removedNodes (1,3), (1,7) are removed
TTN size 12TTN size 14
Info

The TTN codes defined in TenNetLib.jl can readily work, without any changes, for any loop-free tensor networks, e.g., Fork Tensor Networks.

Tip

For 2D systems, use a mapping from the 2D lattice to a 1D chain using Hilbert curve, as shown in Quantum 5, 556 (2021)

diff --git a/v0.1.0/ttn/ttn_12.png b/v0.1.0/ttn/ttn_12.png new file mode 100644 index 0000000..4dc9183 Binary files /dev/null and b/v0.1.0/ttn/ttn_12.png differ diff --git a/v0.1.0/ttn/ttn_14.png b/v0.1.0/ttn/ttn_14.png new file mode 100644 index 0000000..88ecf62 Binary files /dev/null and b/v0.1.0/ttn/ttn_14.png differ diff --git a/v0.1.0/ttn/ttn_gen/index.html b/v0.1.0/ttn/ttn_gen/index.html new file mode 100644 index 0000000..ae2818a --- /dev/null +++ b/v0.1.0/ttn/ttn_gen/index.html @@ -0,0 +1,10 @@ + +Generating TTN · TenNetLib.jl

Generating TTN

TenNetLib.jl defines following functions to generate TTNs with random entries.

For the standard TTN with the default hierarchical binary tree structure, follwoing function can be used.

TenNetLib.default_randomTTNFunction
function default_randomTTN(sites::Vector{Index{T}}, chi::Int, qn::QN = QN()) where T

Returns a TTN object, having random elements, from site Indexs sites, initial bond dimension chi and (optional) global QN sector qn. The structure is a default hierarchical binary tree graph. Automatically handles situations where the number of sites is not a power of 2.

Note: For QN conserving TTN, the bond dimension might be off by one or two from chi.

source

The underlying default binary tree for the function above is generated by the following function.

TenNetLib.default_graph_sitenodesMethod
function default_graph_sitenodes(N::Int)

Given the total number of sites, N::Int, generates the default hierarchical binary tree graph and a Dict{Int, Int2} object that maps each site to the corresponding node. Automatically handles situations where the number of sites is not a power of 2.

Return values:

  • ::Graph{Int2}: Default hierarchical tree graph to accomodate N number of sites in a TTN.
  • ::Dict{Int, Int2}: Maps each site to the corresponding node.

Example:

graph, sitenodes = default_graph_sitenodes(32)
+
+sitenodes[1] == (1,1) # true
+sitenodes[2] == (1,1) # tru
+sitenodes[3] == (1,2) # true
+sitenodes[4] == (1,2) # true
+sitenodes[31] == (1,16) # true
+sitenodes[32] == (1,16) # true
source

In the generic scenario, a random TTN with user-defined structure can be generated by the following function.

TenNetLib.randomTTNFunction
function randomTTN(sites::Vector{Index{T}}, graph::Graph{Int2},
+                   sitenodes::Dict{Int, Int2}, chi::Int, qn::QN = QN()) where T

Returns a TTN object, having random elements, from site Indexs sites, the underlyting graph, sitenodes::Dict{Int, Int2} that maps each site to the corresponding node, initial bond dimension chi, and (optional) global QN sector qn. The structure is determined by the input graph object.

Note: This function can be used to generate any loop-free tensor network.

Note: For QN conserving TTN, the bond dimension might be off by one or two from chi.

source
Info

The above function can be used to generate any loop-free tensor network.

diff --git a/v0.1.0/ttn/ttn_struct/index.html b/v0.1.0/ttn/ttn_struct/index.html new file mode 100644 index 0000000..0c0c9de --- /dev/null +++ b/v0.1.0/ttn/ttn_struct/index.html @@ -0,0 +1,9 @@ + +The TTN object · TenNetLib.jl

The TTN object

TenNetLib.TTNType
mutable struct TTN{T}
+    sites::Vector{Index{T}}
+    graph::Graph{Int2}
+    tensors::Dict{Int2, ITensor}
+    orthocenter::Int2
+end

Tree Tensor Network (TTN) object.

Each tensor is indexed by the tuple of integers (::Int2), (ll, nn), where (usually) ll denotes the layer index and nn denotes the tensor index at each layer.

  • sites::Vector{Index}: Physical site Indexs.
  • graph::Graph{Int2}: Underlying structure of the network defined by Graph{Int2}.
  • tensors::Dict{Int2, ITensor}: Tensors in the TTN.
  • orthocenter::Int2: Orthogonality center of the TTN.
source
ITensors.siteindMethod
function ITensors.siteind(ttn::TTN, n::Int)

Returns the nth site Index of the TTN.

source
TenNetLib.getgraphMethod
function getgraph(ttn::TTN)

Returns (shallow copy of) the underlying graph of the TTN.

source
Base.getindexMethod
function Base.getindex(ttn::TTN, node::Int2)
+function Base.getindex(ttn::TTN, ll::Int, nn::Int)

Returns the tensor at the node::Int2 = (ll, nn).

source
Base.setindex!Method
function Base.setindex!(ttn::TTN, tensor::ITensor, node::Int2)
+function Base.setindex!(ttn::TTN, tensor::ITensor, ll::Int, nn::Int)

Sets the tensor at the node::Int2 = (ll, nn). If the node is not the orthogonality center, orthogonality center is set to (typemin(Int), typemin(Int)).

source
TenNetLib.isvalidnodeMethod
function isvalidnode(ttn::TTN, node::Int2)

Checks whether the input node::Int2 is a valid node in the TTN graph.

source
TenNetLib.isneighborMethod
function isneighbor(ttn::TTN, node1::Int2, node2::Int2)

Checks whether node1 and node2 are neighboring nodes in the TTN.

source
ITensors.findsiteMethod
function ITensors.findsite(ttn::TTN, is)

Returns the first site of the TTN that has at least one Index in common with the Index or ITensor or their collection is.

source
ITensors.findsitesMethod
function ITensors.findsites(ttn::TTN, is)

Returns the sites of the TTN that have Indexs in common with the Index or ITensor or their collection is.

source
TenNetLib.findnodeMethod
function findnode(ttn::TTN, is)

Returns the first node of the TTN that has at least one Index in common with the Index or ITensor or their collection is.

source
TenNetLib.findnodesMethod
function findnodes(ttn::TTN, is)

Returns the nodes of the TTN that have Indexs in common with the Index or ITensor or their collection is.

source
TenNetLib.find_sitenodesMethod
function find_sitenodes(ttn::TTN, ns)

Returns nodes of the TTN that are associated with the sites ns (a collection of Ints).

source
ITensors.maxlinkdimMethod
function ITensors.maxlinkdim(ttn::TTN)

Returns the maximum bond/link dimension of the TTN.

source
LinearAlgebra.normalize!Method
function LinearAlgebra.normalize!(ttn::TTN)

Normalizes the TTN. The TTN must have well-defined orthogonality center.

source
Info

To conserve global symmetry in TTN, TenNetLib.jl uses a dummy index of dimension one whose flux fixes the superselection sector. This dummy index is attached to one of the tensors of TTN, usually the eccentric central node. Unlike MPS, the fluxes of all tensors in TTN are zero.

TenNetLib.find_qnnodeMethod
function find_qnnode(ttn::TTN)

Returns the node where the a dummy QN Index is attached to fix the QN sector. Returns nothing if the TTN does not have QN.

source
TenNetLib.moveisometry_to_next!Method
function moveisometry_to_next!(ttn::TTN, node1::Int2, node2::Int2; kwargs...)

Moves the isometry / orthogonality center of the TTN from node1::Int2 to the neighboring node2::Int. node1 and node2 must be neighboring nodes. node1 must be the orthogonality center unless ignore_orthocenter = true.

Note: Does not normalize the TTN afterwards.

Named arguments and their default values.

  • ignore_orthocenter::Bool = false: If set to true, node1 is not required to be the orthogonality center.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
source
TenNetLib.isometrize_full!Method
function isometrize_full!(ttn::TTN, node::Int2; kwargs...)

Isometrizes the TTN from scratch with respect to the orthogonality center node::Int2.

Named arguments and their default values.

  • normalize::Bool = true: Whether to normalize the TTN afterwards.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
source
TenNetLib.isometrize!Method
function isometrize!(ttn::TTN, node::Int2; kwargs...)

Moves the isometry / orthogonality center of the TTN to a new center node. If the TTN does not have proper orthoginality center, Isometrizes the TTN from scratch.

Named arguments and their default values.

  • normalize::Bool = true: Whether to normalize the TTN afterwards.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".
source
diff --git a/v0.1.0/ttn/update_site_ttn/index.html b/v0.1.0/ttn/update_site_ttn/index.html new file mode 100644 index 0000000..204d8d4 --- /dev/null +++ b/v0.1.0/ttn/update_site_ttn/index.html @@ -0,0 +1,10 @@ + +Perform local updates · TenNetLib.jl

Perform local updates

At the lowest-level of abstraction, TenNetLib.jl allows for updating the StateEnvsTTN for each sites manually.

Skip this part if you want to avoid lower-level abstraction.

TenNetLib.update_position!Method
function update_position!(sysenv::StateEnvsTTN, solver, node::Int2;
+                          time_step::Union{Float64, ComplexF64, Nothing},
+                          normalize::Bool,
+                          maxdim::Int,
+                          mindim::Int,
+                          cutoff::Float64,
+                          svd_alg::String,
+                          kwargs...)

Moves the orthogonality center to pos and update StateEnvsTTN at position pos by solver.

Arguments:

  • sysenv::StateEnvsTTN
  • solver: Solver for update. Currently only eig_solver is supported.
  • pos::Int: Position of the node to be updated.

Named arguments and their default values:

  • time_step::Union{Float64, ComplexF64, Nothing} = nothing: Time step for future functionality.
  • normalize::Bool = true: Whether to normalize after update.
  • maxdim::Int = typemax(Int): Maximum bond dimension after SVD truncation.
  • mindim::Int = 1: Minimum bond dimension after SVD truncation.
  • cutoff::Float64 = Float64_threshold(): Cutoff for SVD truncation.
  • svd_alg::String = "divide_and_conquer".

Named arguments for solver and their default values:

See the documentation of KrylovKit.jl.

  • ishermitian::Bool = true.
  • solver_tol::Float64 = 1E-14.
  • solver_krylovdim::Int = 5.
  • solver_maxiter::Int = 2.
  • solver_outputlevel::Int = 0: See verbosity in KrylovKit.jl.
  • solver_eager::Bool = false.
  • solver_check_convergence::Bool = false.

Return values:

  • ::Float64: Energy.
source

TenNetLib.jl implements the subspace expansion method described in SciPost Phys. Lect. Notes 8 (2019) to increase the bond dimension between two neighboring nodes.

TenNetLib.subspace_expand!Method
function subspace_expand!(psi::TTN, node::Int2, nextnode::Int2,
+                          max_expand_dim::Int, noise::Float64)

Enlarges the bond domension between node and nextnode by max_expand_dim using the subspace expansion. The parameter noise controls stength of the perturbation.

source
diff --git a/versions.js b/versions.js index 4ec0f8f..a038c8a 100644 --- a/versions.js +++ b/versions.js @@ -1,5 +1,7 @@ var DOC_VERSIONS = [ + "stable", + "v0.1", "dev", ]; -var DOCUMENTER_NEWEST = "dev"; -var DOCUMENTER_STABLE = "dev"; +var DOCUMENTER_NEWEST = "v0.1.0"; +var DOCUMENTER_STABLE = "stable";