Correlation energy for the homogeneous electron gas: exact Bethe-Salpeter solution and new approximate evaluation

TL;DR

This paper computes the correlation energy of the homogeneous electron gas using an exact Bethe-Salpeter equation solution and introduces a new approximation, RPAsX, which improves accuracy and stability at low densities.

Contribution

It provides an exact BSE solution for correlation energy and proposes the RPAsX approximation to address low-density instabilities, enhancing previous methods.

Findings

Excellent agreement with Quantum Monte Carlo benchmarks.

RPAsX improves upon the standard BSE kernel.

Addresses imaginary eigenmodes at low densities.

Abstract

The correlation energy of the homogeneous electron gas is evaluated by solving the Bethe-Salpeter equation (BSE) beyond the Tamm-Dancoff approximation for the electronic polarisation propagator. The BSE is expected to improve upon the random phase approximation, owing to the inclusion of exchange diagrams. For instance, since the BSE reduces in second order to M{\o}ller-Plesset perturbation theory, it is self-interaction free in second order. Results for the correlatione energy are compared with Quantum Monte Carlo benchmarks and excellent agreement is observed. For low densities, however, we find imaginary eigenmodes in the polarisation propagator. To avoid the occurence of imaginary eigenmodes, an approximation to the BSE kernel is proposed, which allows to completely remove this issue in the low electron density region. We refer to this approximation as the random phase approximation with screened exchange (RPAsX). We show that this approximation even slightly improves upon the standard BSE kernel.