Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov, and K. Held
Rev. Mod. Phys. 90, 025003 – Published 9 May 2018

Abstract

Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.

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  • Received 31 March 2017

DOI:https://doi.org/10.1103/RevModPhys.90.025003

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

G. Rohringer

  • Russian Quantum Center, 143025 Skolkovo, Russia and Institute for Solid State Physics, TU Wien, 1040 Vienna, Austria

H. Hafermann

  • Mathematical and Algorithmic Sciences Lab, Paris Research Center, Huawei Technologies France SASU, 92100 Boulogne-Billancourt, France

A. Toschi

  • Institute for Solid State Physics, TU Wien, 1040 Vienna, Austria

A. A. Katanin

  • M. N. Mikheev Institute of Metal Physics, Russian Academy of Sciences, 620990 Ekaterinburg, Russia

A. E. Antipov

  • Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA and Department of Physics University of Michigan, Randall Laboratory, Ann Arbor, Michigan 48109-1040, USA

M. I. Katsnelson

  • Radboud University Nijmegen, Institute for Molecules and Materials, NL-6525 AJ Nijmegen, The Netherlands and Ural Federal University, 620002 Ekaterinburg, Russia

A. I. Lichtenstein

  • I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstraße 9, D-20355 Hamburg, Germany and Ural Federal University, 620002 Ekaterinburg, Russia

A. N. Rubtsov

  • Russian Quantum Center, 143025 Skolkovo, Russia and Department of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia

K. Held

  • Institute for Solid State Physics, TU Wien, 1040 Vienna, Austria

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Issue

Vol. 90, Iss. 2 — April - June 2018

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