Ab initio dynamical vertex approximation

TL;DR

This paper introduces an ab initio dynamical vertex approximation method that combines local DMFT correlations with non-local GW and spin fluctuations for more accurate electronic structure calculations.

Contribution

The paper develops and implements an ab initio DΓA approach that captures both local and non-local correlations in materials, extending previous diagrammatic methods.

Findings

Successfully applied to SrVO₃, demonstrating the method's effectiveness.

Naturally includes local DMFT, non-local GW, and additional correlations.

Provides a comprehensive framework for electronic structure beyond existing methods.

Abstract

Diagrammatic extensions of dynamical mean field theory (DMFT) such as the dynamical vertex approximation (D$\Gamma$A) allow us to include non-local correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an AbinitioD$\Gamma$A approach for electronic structure calculations of materials. Starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare non-local Coulomb interaction and all local vertex corrections. From this we calculate the full non-local vertex and the non-local self-energy through the Bethe-Salpeter equation. The AbinitioD$\Gamma$A approach naturally generates all local DMFT correlations and all non-local $GW$ contributions, but also further non-local correlations beyond: mixed terms of the former two and non-local spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO$_3$.