Linear-time generalized Hartree-Fock algorithm for quasi-one-dimensional systems

TL;DR

This paper introduces a linear-time algorithm for generalized Hartree-Fock calculations in quasi-one-dimensional fermionic systems, significantly improving computational efficiency while maintaining accuracy.

Contribution

The authors develop a novel linear-time algorithm for generalized Hartree-Fock in quasi-1D systems using Gaussian fermionic matrix product states, enhancing scalability.

Findings

Scales approximately linearly with system size for quasi-1D systems

Maintains accuracy comparable to traditional cubic-scaling methods

Effective for Hubbard models with inhomogeneous potentials

Abstract

In many approximate approaches to fermionic quantum many-body systems, such as Hartree-Fock and density functional theory, solving a system of non-interacting fermions coupled to some effective potential is the computational bottleneck. In this paper, we demonstrate that this crucial computational step can be accelerated using recently developed methods for Gaussian fermionic matrix product states (GFMPS). As an example, we study the generalized Hartree-Fock method, which unifies Hartree-Fock and self-consistent BCS theory, applied to Hubbard models with an inhomogeneous potential. We demonstrate that for quasi-one-dimensional systems with local interactions, our approach scales approximately linearly in the length of the system while yielding a similar accuracy to standard approaches that scale cubically in the system size.