GW approximation with self-screening correction

TL;DR

This paper identifies and corrects the self-screening error in the GW approximation, improving its accuracy for systems like the hydrogen atom by incorporating exchange diagrams, demonstrated on a hydrogen dimer model.

Contribution

The authors introduce a scheme to eliminate self-screening in GW approximation, aligning it with exchange diagram inclusion, and validate it on a hydrogen dimer model.

Findings

The scheme removes self-screening error in GW approximation.

It yields exact results to second order in a Hubbard model.

Validated on a hydrogen dimer system.

Abstract

The \emph{GW} approximation takes into account electrostatic self-interaction contained in the Hartree potential through the exchange potential. However, it has been known for a long time that the approximation contains self-screening error as evident in the case of the hydrogen atom. When applied to the hydrogen atom, the \emph{GW} approximation does not yield the exact result for the electron removal spectra because of the presence of self-screening: the hole left behind is erroneously screened by the only electron in the system which is no longer present. We present a scheme to take into account self-screening and show that the removal of self-screening is equivalent to including exchange diagrams, as far as self-screening is concerned. The scheme is tested on a model hydrogen dimer and it is shown that the scheme yields the exact result to second order in $(U_{0}-U_{1})/2t$ where $U_{0}$ and $U_{1}$ are respectively the onsite and offsite Hubbard interaction parameters and $t$ the hopping parameter.