Dynamical vertex approximation -- an introduction

Abstract

We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D$Γ$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$Γ$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.

An elementary introduction to dynamical vertex approximation given at the YKIS 2007 conference in Kyoto, Japan. 17 pages, 14 figures in 19 eps files