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+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>DMRG · ITensors.jl</title><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script><link href="assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="index.html"><img src="assets/logo.png" alt="ITensors.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="index.html">ITensors.jl</a></span></div><form class="docs-search" action="search.html"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="index.html">Introduction</a></li><li><span class="tocitem">Getting Started with ITensor</span><ul><li><a class="tocitem" href="getting_started/Installing.html">Installing Julia and ITensor</a></li><li><a class="tocitem" href="getting_started/RunningCodes.html">Running ITensor and Julia Codes</a></li><li><a class="tocitem" href="getting_started/DebugChecks.html">Enabling Debug Checks</a></li><li><a class="tocitem" href="getting_started/NextSteps.html">Next Steps</a></li></ul></li><li><span class="tocitem">Tutorials</span><ul><li><a class="tocitem" href="tutorials/DMRG.html">DMRG</a></li><li><a class="tocitem" href="tutorials/QN_DMRG.html">Quantum Number Conserving DMRG</a></li><li><a class="tocitem" href="tutorials/MPSTimeEvolution.html">MPS Time Evolution</a></li></ul></li><li><span class="tocitem">Code Examples</span><ul><li><a class="tocitem" href="examples/ITensor.html">ITensor Examples</a></li><li><a class="tocitem" href="examples/MPSandMPO.html">MPS and MPO Examples</a></li><li><a class="tocitem" href="examples/DMRG.html">DMRG Examples</a></li><li><a class="tocitem" href="examples/Physics.html">Physics (SiteType) System Examples</a></li></ul></li><li><span class="tocitem">Documentation</span><ul><li><a class="tocitem" href="IndexType.html">Index</a></li><li><a class="tocitem" href="IndexSetType.html">Index collections</a></li><li><a class="tocitem" href="ITensorType.html">ITensor</a></li><li><a class="tocitem" href="MPSandMPO.html">MPS and MPO</a></li><li><a class="tocitem" href="QN.html">QN</a></li><li><a class="tocitem" href="SiteType.html">SiteType and op, state, val functions</a></li><li><a class="tocitem" href="IncludedSiteTypes.html">SiteTypes Included with ITensor</a></li><li><input class="collapse-toggle" id="menuitem-5-8" type="checkbox" checked/><label class="tocitem" for="menuitem-5-8"><span class="docs-label">DMRG</span><i class="docs-chevron"></i></label><ul class="collapsed"><li class="is-active"><a class="tocitem" href="DMRG.html">DMRG</a></li><li><a class="tocitem" href="Sweeps.html">Sweeps</a></li><li><a class="tocitem" href="ProjMPO.html">ProjMPO</a></li><li><a class="tocitem" href="ProjMPOSum.html">ProjMPOSum</a></li><li><a class="tocitem" href="Observer.html">Observer System for DMRG</a></li><li><a class="tocitem" href="DMRGObserver.html">DMRGObserver</a></li></ul></li><li><a class="tocitem" href="OpSum.html">OpSum (AutoMPO)</a></li></ul></li><li><span class="tocitem">Frequently Asked Questions</span><ul><li><a class="tocitem" href="faq/JuliaAndCpp.html">Programming Language (Julia, C++, ...) 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+dmrg(H::MPO, psi0::MPS, sweeps::Sweeps; kwargs...)</code></pre><p>Use the density matrix renormalization group (DMRG) algorithm to optimize a matrix product state (MPS) such that it is the eigenvector of lowest eigenvalue of a Hermitian matrix <code>H</code>, represented as a matrix product operator (MPO).</p><pre><code class="nohighlight hljs">dmrg(Hs::Vector{MPO}, psi0::MPS; kwargs...)
+dmrg(Hs::Vector{MPO}, psi0::MPS, sweeps::Sweeps; kwargs...)</code></pre><p>Use the density matrix renormalization group (DMRG) algorithm to optimize a matrix product state (MPS) such that it is the eigenvector of lowest eigenvalue of a Hermitian matrix <code>H</code>. This version of <code>dmrg</code> accepts a representation of H as a Vector of MPOs, <code>Hs = [H1, H2, H3, ...]</code> such that <code>H</code> is defined <code>as H = H1 + H2 + H3 + ...</code> Note that this sum of MPOs is not actually computed; rather the set of MPOs <code>[H1,H2,H3,..]</code> is efficiently looped over at each step of the DMRG algorithm when optimizing the MPS.</p><pre><code class="nohighlight hljs">dmrg(H::MPO, Ms::Vector{MPS}, psi0::MPS; weight=1.0, kwargs...)
+dmrg(H::MPO, Ms::Vector{MPS}, psi0::MPS, sweeps::Sweeps; weight=1.0, kwargs...)</code></pre><p>Use the density matrix renormalization group (DMRG) algorithm to optimize a matrix product state (MPS) such that it is the eigenvector of lowest eigenvalue of a Hermitian matrix <code>H</code>, subject to the constraint that the MPS is orthogonal to each of the MPS provided in the Vector <code>Ms</code>. The orthogonality constraint is approximately enforced by adding to <code>H</code> terms of the form <code>w|M1&gt;&lt;M1| + w|M2&gt;&lt;M2| + ...</code> where <code>Ms=[M1, M2, ...]</code> and <code>w</code> is the &quot;weight&quot; parameter, which can be adjusted through the optional <code>weight</code> keyword argument.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p><code>dmrg</code> will report the energy of the operator <code>H + w|M1&gt;&lt;M1| + w|M2&gt;&lt;M2| + ...</code>, not the operator <code>H</code>. If you want the expectation value of the MPS eigenstate with respect to just <code>H</code>, you can compute it yourself with an observer or after DMRG is run with <code>inner(psi&#39;, H, psi)</code>.</p></div></div><p>The MPS <code>psi0</code> is used to initialize the MPS to be optimized.</p><p>The number of sweeps of thd DMRG algorithm is controlled by passing the <code>nsweeps</code> keyword argument. The keyword arguments <code>maxdim</code>, <code>cutoff</code>, <code>noise</code>, and <code>mindim</code> can also be passed to control the cost versus accuracy of the algorithm - see below for details.</p><p>Alternatively the number of sweeps and accuracy parameters can be passed through a <code>Sweeps</code> object, though this interface is no longer preferred.</p><p>Returns:</p><ul><li><code>energy::Number</code> - eigenvalue of the optimized MPS</li><li><code>psi::MPS</code> - optimized MPS</li></ul><p>Keyword arguments:</p><ul><li><code>nsweeps::Int</code> - number of &quot;sweeps&quot; of DMRG to perform</li></ul><p>Optional keyword arguments:</p><ul><li><code>maxdim</code> - integer or array of integers specifying the maximum size  allowed for the bond dimension or rank of the MPS being optimized.</li><li><code>cutoff</code> - float or array of floats specifying the truncation error cutoff  or threshold to use for truncating the bond dimension or rank of the MPS.</li><li><code>eigsolve_krylovdim::Int = 3</code> - maximum dimension of Krylov space used to  locally solve the eigenvalue problem. Try setting to a higher value if  convergence is slow or the Hamiltonian is close to a critical point. <sup class="footnote-reference"><a id="citeref-krylovkit" href="#footnote-krylovkit">[krylovkit]</a></sup></li><li><code>eigsolve_tol::Number = 1e-14</code> - Krylov eigensolver tolerance. <sup class="footnote-reference"><a id="citeref-krylovkit" href="#footnote-krylovkit">[krylovkit]</a></sup></li><li><code>eigsolve_maxiter::Int = 1</code> - number of times the Krylov subspace can be  rebuilt. <sup class="footnote-reference"><a id="citeref-krylovkit" href="#footnote-krylovkit">[krylovkit]</a></sup></li><li><code>eigsolve_verbosity::Int = 0</code> - verbosity level of the Krylov solver.  Warning: enabling this will lead to a lot of outputs to the terminal. <sup class="footnote-reference"><a id="citeref-krylovkit" href="#footnote-krylovkit">[krylovkit]</a></sup></li><li><code>ishermitian=true</code> - boolean specifying if dmrg should assume the MPO (or more  general linear operator) represents a Hermitian matrix. <sup class="footnote-reference"><a id="citeref-krylovkit" href="#footnote-krylovkit">[krylovkit]</a></sup></li><li><code>noise</code> - float or array of floats specifying strength of the &quot;noise term&quot;  to use to aid convergence.</li><li><code>mindim</code> - integer or array of integers specifying the minimum size of the  bond dimension or rank, if possible.</li><li><code>outputlevel::Int = 1</code> - larger outputlevel values make DMRG print more  information and 0 means no output.</li><li><code>observer</code> - object implementing the <a href="Observer.html#observer">Observer</a> interface  which can perform measurements and stop DMRG early.</li><li><code>write_when_maxdim_exceeds::Int</code> - when the allowed maxdim exceeds this  value, begin saving tensors to disk to free RAM memory in large calculations</li><li><code>write_path::String = tempdir()</code> - path to use to save files to disk  (to save RAM) when maxdim exceeds the <code>write_when_maxdim_exceeds</code> option, if set</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/ITensor/ITensors.jl/blob/f35bee8c4fb4dfe3ac4c6b84a3113f510adfb613/src/mps/dmrg.jl#L57-L155">source</a></section></article><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-krylovkit"><a class="tag is-link" href="#citeref-krylovkit">krylovkit</a>The <code>dmrg</code> function in <code>ITensors.jl</code> currently uses the <code>eigsolve</code> function in <code>KrylovKit.jl</code> as the internal the eigensolver. See the <code>KrylovKit.jl</code> documention on the <code>eigsolve</code> function for more details: <a href="https://jutho.github.io/KrylovKit.jl/stable/man/eig/#KrylovKit.eigsolve">KrylovKit.eigsolve</a>.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="IncludedSiteTypes.html">« SiteTypes Included with ITensor</a><a class="docs-footer-nextpage" href="Sweeps.html">Sweeps »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Wednesday 15 November 2023 00:09">Wednesday 15 November 2023</span>. 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