Dynamical vertex approximation - An introduction -

Karsten Held, Andrey A. Katanin, Alessandro Toschi

Research output: Contribution to journalArticlepeer-review

58 Citations (Scopus)


We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (DΓA). 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, Df1A 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.

Original languageEnglish
Pages (from-to)117-133
Number of pages17
JournalProgress of Theoretical Physics Supplement
Issue number176
Publication statusPublished - 2008
Externally publishedYes


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