Spatial non-locality of electronic correlations beyond GW approximation

TL;DR

This study investigates the spatial non-locality of electronic correlations beyond the GW approximation using momentum-dependent calculations, revealing significant non-local effects that challenge the locality assumption in GW+DMFT methods.

Contribution

First direct analysis of spatial non-locality of electronic correlations beyond GW using momentum-dependent and local approximations within the GW+G3W2 framework.

Findings

Non-local effects are strong in NiO, α-Ce, and LiFeAs.

Non-locality is crucial for accurate vertex corrections.

Local approximation in GW+DMFT may be insufficient.

Abstract

The question of spatial locality of electronic correlations beyond GW approximation is one of the central issues of the famous combination of GW and dynamical mean field theory, GW+DMFT. In this work, the above question is addressed directly (for the first time) by performing calculations with and without assumption of locality of the corresponding diagrams. For this purpose we use sc(GW+G3W2) approach where the higher order part (G3W2) is evaluated with fully momentum dependent Green's function G and screened interaction W and with "local" variant, where the single site approximation is assumed for both G and W. For all three materials studied in this work (NiO, $\alpha$-Ce, LiFeAs), we have found the spatial non-locality effects to be strong. For NiO and LiFeAs they, in fact, are decisive for the proper evaluation of vertex corrections. The results of this study have direct impact on our understanding of approximations made in practical implementations of GW+DMFT method, where all diagrams beyond GW (DMFT part) are assumed to be local. Taking into account the fact that the first diagrams beyond GW represent the most important contribution also in GW+DMFT calculations, we conclude that the basic assumption of GW+DMFT, namely the locality of diagrams evaluated in the DMFT part, is not as good as it is believed to be.