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Dynamical vertex approximation -- an introduction

Author: K. Held, A. A. Katanin, A. Toschi
Url: http://arxiv.org/abs/0807.1860
Format: Ps, Pdf
Year: 2008
Category: DMFT
Pages: 17
Clicks: 665

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.

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