GW{\Gamma} + Bethe-Salpeter equation approach for photoabsorption spectra: Importance of self-consistent GW{\Gamma} calculations in small atomic systems

TL;DR

This paper introduces a self-consistent GW{ extGamma} + Bethe-Salpeter equation approach that improves the accuracy of photoabsorption spectra calculations in small atomic systems by ensuring gauge invariance and better treatment of vertex corrections.

Contribution

The paper develops a self-consistent GW{ extGamma} method combined with BSE that satisfies gauge invariance and enhances photoabsorption spectrum predictions over standard methods.

Findings

Significant redshift correction in PAS for Na, Na3, B2, and C2H2.

Improved agreement with experimental PAS compared to G0W0+BSE.

PES are already well reproduced in G0W0, but PAS benefits from the new method.

Abstract

The self-consistent GW{\Gamma} method satisfies the Ward-Takahashi identity (i.e., the gauge invariance or the local charge continuity) for arbitrary energy ($\omega$) and momentum ($\bf q$) transfers. Its self-consistent first-principles treatment of the vertex $\Gamma=\Gamma_v$ or $\Gamma_W$ is possible to first order in the bare ($v$) or dynamically-screened ($W$) Coulomb interaction. It is developed within a linearized scheme and combined with the Bethe-Salpeter equation (BSE) to accurately calculate photoabsorption spectra (PAS) and photoemission (or inverse photoemission) spectra (PES) simultaneously. The method greatly improves the PAS of Na, Na$_3$, B$_2$, and C$_2$H$_2$ calculated using the standard one-shot $G_0W_0$ + BSE method that results in significantly redshifted PAS by 0.8-3.1 eV, although the PES are well reproduced already in $G_0W_0$.