Assessment of the GW approximation using Hubbard chains

TL;DR

This paper evaluates the accuracy of the GW approximation against exact results in small Hubbard chains, analyzing the effects of chemical potentials and numerical broadening to improve many-body perturbation calculations.

Contribution

It provides a detailed comparison of GW approximation performance with exact solutions in Hubbard chains, highlighting how to enhance computational methods.

Findings

GW approximation accuracy varies with band filling and correlation strength.

Proper treatment of chemical potentials improves GW results.

Numerical resonance broadening impacts the reliability of calculations.

Abstract

We investigate the performance of the GW approximation by comparison to exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are examined, and we show how a proper treatment can improve computational implementations of many-body perturbation theory in general. GW and exchange-only calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable.