Dynamical vertex approximation -- an introduction

K. Held; A. A. Katanin; A. Toschi

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arXiv · 0807.1860

Dynamical vertex approximation -- an introduction

K. Held·A. A. Katanin·A. Toschi

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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.

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K. Held, A. A. Katanin, A. Toschi. 2008-07-11. Dynamical vertex approximation -- an introduction. https://arxiv.org/abs/0807.1860

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