Post-$GW$ theory and its application to pseudogap in strongly correlated system

TL;DR

This paper introduces a systematic extension of the $GW$ approximation, called Post-$GW$ theory, which improves the description of pseudogap phenomena in strongly correlated systems by reconnecting the screened potential to the physical response function.

Contribution

It develops a new theoretical framework for Green's function corrections that overcomes limitations of the $GW$ approximation, especially in capturing pseudogap behavior.

Findings

Significant qualitative and quantitative improvements over standard $GW$

Successful capture of pseudogap phenomena in the 2D Hubbard model

Enhanced accuracy in spectral function and charge compressibility calculations

Abstract

The $GW$ approximation is a widely used framework for studying correlated materials, but it struggles with certain limitations, such as its inability to explain pseudogap phenomena. To overcome these problems, we propose a systematic theoretical framework for Green's function corrections and apply it specifically to the $GW$ approximation. In this new theory, the screened potential is reconnected to the physical response function, i.e. the covariant response function proposed in \cite{cGW_2023}, rather than using the RPA formula. We apply our scheme to calculate Green's function, the spectral function, and the charge compressibility in the two-dimensional Hubbard model. Our scheme yields significant qualitative and quantitative improvements over the standard $GW$ method and successfully captures the pseudogap behavior.