H-wave -- A Python package for the Hartree-Fock approximation and the random phase approximation

TL;DR

H-wave is an open-source Python package that facilitates Hartree-Fock and RPA calculations for various fermionic Hamiltonians, enabling stability analysis and susceptibility calculations in condensed matter physics.

Contribution

The paper introduces H-wave, a versatile software package that simplifies HFA and RPA computations for standard and ab initio Hamiltonians, with user-friendly input formats and practical examples.

Findings

Performed zero-temperature HFA on extended Hubbard model

Conducted finite-temperature HFA on cubic lattice

Applied RPA to extended Hubbard model on square lattice

Abstract

H-wave is an open-source software package for performing the Hartree--Fock approximation (HFA) and random phase approximation (RPA) for a wide range of Hamiltonians of interacting fermionic systems. In HFA calculations, H-wave examines the stability of several symmetry-broken phases, such as anti-ferromagnetic and charge-ordered phases, in the given Hamiltonians at zero and finite temperatures. Furthermore, H-wave calculates the dynamical susceptibilities using RPA to examine the instability toward the symmetry-broken phases. By preparing a simple input file for specifying the Hamiltonians, users can perform HFA and RPA for standard Hamiltonians in condensed matter physics, such as the Hubbard model and its extensions. Additionally, users can use a Wannier90-like format to specify fermionic Hamiltonians. A Wannier90 format is implemented in RESPACK to derive ab initio Hamiltonians for solids. HFA and RPA for the ab initio Hamiltonians can be easily performed using H-wave. In this paper, we first explain the basis of HFA and RPA, and the basic usage of H-wave, including download and installation. Thereafter, the input file formats implemented in H-wave, including the Wannier90-like format for specifying the interacting fermionic Hamiltonians, are discussed. Finally, we present several examples of H-wave such as zero-temperature HFA calculations for the extended Hubbard model on a square lattice, finite-temperature HFA calculations for the Hubbard model on a cubic lattice, and RPA in the extended Hubbard model on a square lattice.