Approximating the ground state of fermion system by multiple determinant states: matching pursuit approach

TL;DR

This paper introduces a stable numerical method using a matching pursuit algorithm to approximate the ground state of fermion systems with multiple determinant states, starting from Hartree-Fock and demonstrated on the 2D Hubbard model.

Contribution

It presents a novel matching pursuit-based approach for systematically improving ground state approximations with multiple determinants.

Findings

Effective in approximating the ground state of the 2D Hubbard model

Starts from Hartree-Fock and iteratively improves the state

Stable and simple numerical implementation

Abstract

We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit algorithm. The first determinant state is identical to that of the Hartree-Fock theory. Calculations for two-dimensional Hubbard model serve as a demonstration.