# HartreeFockBogoliubov.jl Documentation

## Overview

HartreeFockBogoliubov.jl is a Julia package for solving interacting fermion Hamiltonian using Hartree-Fock-Bogoliubov (HFB) approach. This project aims to assist fast development of HFB solver for a generic Hamiltonian of the form

$$$\mathcal{H} = \sum_{\alpha,\beta} c_{\alpha}^{\dagger} t_{\alpha\beta} c_{\beta} + \frac{1}{2} \sum_{\alpha,\beta,\gamma,\delta} V_{\alpha\beta\gamma\delta} c_{\alpha}^{\dagger} c_{\beta}^{\dagger} c_{\delta} c_{\gamma}$$$

## Installation

HartreeFockBogoliubov.jl is not a registered package. Install it by

HartreeFockBogoliubov.jl is currently not registered in the Julia Package Listing. To install, type

add https://github.com/kyungminlee/HartreeFockBogoliubov.jl

to Julia's package manager.

## Usage

To construct HFB solver

1. Specify a unitcell, i.e. the lattice constants.
2. Specify the "orbitals" of the unitcell, and their locations. Here the word "orbital" refers to any fermionic degrees of freedom, and includes sites, orbitals in the conventional sense, and spins, etc.
3. Specify the hoppings between the orbitals, together with their real-space displacements. The displacement is required since, with the periodic boundary condition, hopping from orbital α to orbital β within the same unitcell is different from the hopping from orbital α to β in different unitcells.
4. Specify the interactions. As for the hoppings, you need to specify the orbitals and the displacement of the interactions.
5. The full interacting Hamiltonian constructed so far can be passed to a HFBSolver which decomposes it into different HFB channels.

MIT License

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