Dynamical vertex approximation - a step beyond dynamical mean field theory

TL;DR

This paper introduces the dynamical vertex approximation, a diagrammatic method that extends dynamical mean field theory to include nonlocal correlations, enabling better modeling of phenomena like magnons and localization in strongly correlated materials.

Contribution

It develops a new diagrammatic approach combining local and nonlocal self-energy diagrams based on the local irreducible vertex, advancing beyond traditional dynamical mean field theory.

Findings

Describes (para-)magnons and weak localization effects

Analyzes the interplay between nonlocal antiferromagnetic and local correlations near Mott transition

Provides a framework for studying long-range correlations in strongly correlated systems

Abstract

We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean field theory and long-range correlations beyond. It allows for example to describe (para-)magnons and weak localization effects in strongly correlated systems. As a first application, we study the interplay between nonlocal antiferromagnetic correlations and the strong local correlations emerging in the vicinity of a Mott-Hubbard transition.