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Workflow

This template file helps in annotating Hartree-Fock Mean-Field theory papers by providing a collection of prompts, which should be followed in a specific order based on the type of the paper.

We categorized the papers based on:

  • Hamiltonian: continuum | lattice
  • Formalism: first-quantized | second-quantized
  • Order parameter: Hartree | Fock | Hartree-Fock

Note: The combination of 'lattice' and 'first-quantized' is incompatible.

Detailed workflows for each paper category are as follows:

lattice, second-quantized, Hartree

L_2_H Example: 1106.6060

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (lattice version)"]
        b2["Construct interaction Hamiltonian (real space, lattice version)"]
        b3["Convert noninteracting Hamiltonian in real space to momentum space (lattice version)"]
        b4["Convert interacting Hamiltonian in real space to momentum space (lattice version)"]
        b1-->b2
        b2-->b3
        b3-->b4
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph D["Order parameters"]
        direction TB
        d1["Hartree term only"]
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index only"]
        e3["Reduce momentum in Hartree term (momentum in BZ)"]
        e4["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
    end
    A==>B
    B==>C
    C==>D
    D==>E
Loading

lattice, second-quantized, Fock

L_2_F

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (lattice version)"]
        b2["Construct interaction Hamiltonian (real space, lattice version)"]
        b3["Convert noninteracting Hamiltonian in real space to momentum space (lattice version)"]
        b4["Convert interacting Hamiltonian in real space to momentum space (lattice version)"]
        b1-->b2
        b2-->b3
        b3-->b4
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph D["Order parameters"]
        direction TB
        d1["Fock term only"]
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index only"]
        e3["Reduce momentum in Fock term (momentum in BZ)"]
        e4["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
    end
    A==>B
    B==>C
    C==>D
    D==>E
Loading

lattice, second-quantized, Hartree-Fock

L_2_HF Example: 2004.04168

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (lattice version)"]
        b2["Construct interaction Hamiltonian (real space, lattice version)"]
        b3["Convert noninteracting Hamiltonian in real space to momentum space (lattice version)"]
        b4["Convert interacting Hamiltonian in real space to momentum space (lattice version)"]
        b1-->b2
        b2-->b3
        b3-->b4
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index only"]
        e3["Reduce momentum in Hartree term (momentum in BZ)"]
        e4["Reduce momentum in Fock term (momentum in BZ)"]
        e5["Combine the Hartree and Fock term"]
        e6["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
        e4-->e5
        e5-->e6
    end
    A==>B
    B==>C
    C==>E
Loading

continuum, first-quantized, Hartree

C_1_H

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (continuum version, single-particle)"]
        b2["Define each term in Kinetic Hamiltonian (continuum version)"]
        b3["Construct Potential Hamiltonian (continuum version)"]
        b4["Define each term in Potential Hamiltonian (continuum version)"]
        b5["Convert from single-particle to second-quantized form, return in matrix "]
        b6["Convert from single-particle to second-quantized form, return in summation (expand the matrix)"]
        b7["Convert noninteracting Hamiltonian in real space to momentum space (continuum version)"]
        b8["Construct interaction Hamiltonian (momentum space)"]
        b1-->b2
        b2-->b3
        b3-->b4
        b4-->b5
        b5-->b6
        b6-->b7
        b7-->b8
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph D["Order parameters"]
        direction TB
        d1["Hartree term only"]
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index to combine Hartree and Fock terms"]
        e3["Reduce momentum in Hartree term (momentum in BZ + reciprocal lattice)"]
        e4["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
    end
    A==>B
    B==>C
    C==>D
    D==>E
Loading

continuum, first-quantized, Fock

C_1_F

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (continuum version, single-particle)"]
        b2["Define each term in Kinetic Hamiltonian (continuum version)"]
        b3["Construct Potential Hamiltonian (continuum version)"]
        b4["Define each term in Potential Hamiltonian (continuum version)"]
        b5["Convert from single-particle to second-quantized form, return in matrix"]
        b6["Convert from single-particle to second-quantized form, return in summation (expand the matrix)"]
        b7["Convert noninteracting Hamiltonian in real space to momentum space (continuum version)"]
        b8["Construct interaction Hamiltonian (momentum space)"]
        b1-->b2
        b2-->b3
        b3-->b4
        b4-->b5
        b5-->b6
        b6-->b7
        b7-->b8
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph D["Order parameters"]
        direction TB
        d1["Fock term only"]
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index to combine Hartree and Fock terms"]
        e3["Reduce momentum in Fock term (momentum in BZ + reciprocal lattice)"]
        e4["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
    end
    A==>B
    B==>C
    C==>D
    D==>E
Loading

continuum, first-quantized, Hartree-Fock

C_1_HF Example: 2111.01152, 1812.04213

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (continuum version, single-particle)"]
        b2["Define each term in Kinetic Hamiltonian (continuum version)"]
        b3["Construct Potential Hamiltonian (continuum version)"]
        b4["Define each term in Potential Hamiltonian (continuum version)"]
        b5["Convert from single-particle to second-quantized form, return in matrix"]
        b6["Convert from single-particle to second-quantized form, return in summation (expand the matrix)"]
        b7["Convert noninteracting Hamiltonian in real space to momentum space (continuum version)"]
        b8["Construct interaction Hamiltonian (momentum space)"]
        b1-->b2
        b2-->b3
        b3-->b4
        b4-->b5
        b5-->b6
        b6-->b7
        b7-->b8
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index to combine Hartree and Fock terms"]
        e3["Reduce momentum in Hartree term (momentum in BZ + reciprocal lattice)"]
        e4["Reduce momentum in Fock term (momentum in BZ + reciprocal lattice)"]
        e5["Combine the Hartree and Fock term"]
        e6["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
        e4-->e5
        e5-->e6
    end
    A==>B
    B==>C
    C==>E
Loading

continuum, second-quantized, Hartree

C_2_H

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (continuum version, second-quantized)"]
        b2["Define each term in Kinetic Hamiltonian (continuum version)"]
        b3["Construct Potential Hamiltonian (continuum version)"]
        b4["Define each term in Potential Hamiltonian (continuum version)"]
        b7["Convert noninteracting Hamiltonian in real space to momentum space (continuum version)"]
        b8["Construct interaction Hamiltonian (momentum space)"]
        b1-->b2
        b2-->b3
        b3-->b4
        b4-->b7
        b7-->b8
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph D["Order parameters"]
        direction TB
        d1["Hartree term only"]
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index to combine Hartree and Fock terms"]
        e3["Reduce momentum in Hartree term (momentum in BZ + reciprocal lattice)"]
        e4["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
    end
    A==>B
    B==>C
    C==>D
    D==>E
Loading

continuum, second-quantized, Fock

C_2_F

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (continuum version, second-quantized)"]
        b2["Define each term in Kinetic Hamiltonian (continuum version)"]
        b3["Construct Potential Hamiltonian (continuum version)"]
        b4["Define each term in Potential Hamiltonian (continuum version)"]
        b7["Convert noninteracting Hamiltonian in real space to momentum space (continuum version)"]
        b8["Construct interaction Hamiltonian (momentum space)"]
        b1-->b2
        b2-->b3
        b3-->b4
        b4-->b7
        b7-->b8
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph D["Order parameters"]
        direction TB
        d1["Fock term only"]
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index to combine Hartree and Fock terms"]
        e3["Reduce momentum in Fock term (momentum in BZ + reciprocal lattice)"]
        e4["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
    end
    A==>B
    B==>C
    C==>D
    D==>E
Loading

continuum, second-quantized, Hartree-Fock

C_2_HF Example: 2108.02159

flowchart LR
    subgraph A["Preamble"]
        direction TB
        a1["Preamble"]
    end
    subgraph B["Hamiltonian construction"]
        direction TB
        b1["Construct Kinetic Hamiltonian (continuum version, second-quantized)"]
        b2["Define each term in Kinetic Hamiltonian (continuum version)"]
        b3["Construct Potential Hamiltonian (continuum version)"]
        b4["Define each term in Potential Hamiltonian (continuum version)"]
        b7["Convert noninteracting Hamiltonian in real space to momentum space (continuum version)"]
        b8["Construct interaction Hamiltonian (momentum space)"]
        b1-->b2
        b2-->b3
        b3-->b4
        b4-->b7
        b7-->b8
    end
    subgraph C["Mean-field theory"]
        direction TB
        c1["Wick's theorem"]
        c2["Extract quadratic term"]
        c1-->c2
    end
    subgraph E["Simplify the MF quadratic term"]
        direction TB
        e1["Expand interaction"]
        e2["Swap the index to combine Hartree and Fock terms"]
        e3["Reduce momentum in Hartree term (momentum in BZ + reciprocal lattice)"]
        e4["Reduce momentum in Fock term (momentum in BZ + reciprocal lattice)"]
        e5["Combine the Hartree and Fock term"]
        e6["Construct full Hamiltonian after HF"]
        e1-->e2
        e2-->e3
        e3-->e4
        e4-->e5
        e5-->e6
    end
    A==>B
    B==>C
    C==>E
Loading