Improvement on the GW$\Gamma$ Scheme for the Electron Self-Energy and Relevance of the $G_0W_0$ Approximation from this Perspective

TL;DR

This paper introduces an improved self-consistent scheme for calculating electron self-energy that satisfies the Ward identity, demonstrating that the one-shot G0W0 approximation effectively captures key vertex and self-energy corrections.

Contribution

An enhanced self-consistent calculation scheme for electron self-energy that improves computational efficiency and applicability, clarifying the relevance of G0W0 approximation.

Findings

The scheme satisfies the Ward identity.

G0W0 approximation accounts for vertex and self-energy corrections.

Quasiparticle dispersion matches G0W0 results for semiconductors and insulators.

Abstract

Based on an exact functional form derived for the three-point vertex function $\Gamma$, we propose a self-consistent calculation scheme for the electron self-energy with $\Gamma$ always satisfying the Ward identity. This scheme is basically equivalent to the one proposed in 2001, but it is improved in the aspects of computational costs and its applicability range; it can treat a low-density electron system with a dielectric catastrophe. If it is applied to semiconductors and insulators, we find that the obtained quasiparticle dispersion is virtually the same as that in the one-shot $GW$ approximation (or $G_0W_0$A), indicating that the $G_0W_0$A actually takes proper account of both vertex and high-order self-energy corrections in a mutually cancelling manner.