Dynamical vertex approximation -- an introduction

TL;DR

The paper introduces the dynamical vertex approximation (DΓA), a diagrammatic extension of DMFT that captures both local and non-local correlations, enabling the study of complex phenomena in strongly correlated electron systems.

Contribution

It provides an elementary introduction to DΓA, highlighting its ability to incorporate non-local correlations beyond DMFT for the first time.

Findings

DΓA captures quasiparticle renormalizations and Mott-Hubbard transitions.

It describes phenomena like magnons, quantum criticality, and interplay of magnetism and superconductivity.

Results for the Hubbard model in 1D, 2D, and 3D are reviewed.

Abstract

We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D$\Gamma$A). This approach contains the important local correlations of DMFT, giving, among others, rise to quasiparticle renormalizations, Mott-Hubbard transitions and magnetism, but also non-local correlations beyond. The latter are at the very essence of many physical phenomena in strongly correlated elecectron systems. As correlations are treated equally on all length scales, D$\Gamma$A allows us to describe physical phenomena such as magnons, quantum criticality, and the interplay between antiferromagnetism and superconductivity. We review results hitherto obtained for the Hubbard model in dimensions d=3, 2, and 1.