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Strong Electronic Correlations: Dynamical Mean-Field Theory and Beyond

  • Hartmut Hafermann
  • Frank Lechermann
  • Alexei N. Rubtsov
  • Mikhail I. Katsnelson
  • Antoine Georges
  • Alexander I. Lichtenstein
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 843)

Abstract

This chapter aims at a pedagogical introduction to theoretical approaches of strongly correlated materials based on dynamical mean-field theory (DMFT) and its extensions. The goal of this theoretical construction is to retain the many-body aspects of local atomic physics within the extended solid. After introducing the main concept at the level of the Hubbard model, we briefly review the theoretical insights into the Mott metal-insulator transition that DMFT provides. We then describe realistic extensions of this approach which combine the accuracy of first-principle Density-Functional Theory with the treatment of local many-body effects within DMFT. We further provide an elementary discussion of the continuous-time Quantum Monte Carlo schemes for the numerical solution of the DMFT effective quantum impurity problem. Finally, the effects of short-range non-local correlations within cluster extensions of the DMFT scheme, as well as long-range fluctuations within the fully renormalized dual-fermion perturbation scheme are discussed extensively.

Keywords

Green Function Local Density Approximation Mott Transition Lattice Fermion Density Matrix Renormalization Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We are greatly indebted to the input of our collaborators and colleagues Markus Aichhorn, Vladimir Anisimov, Matthias Balzer, Silke Biermann, Lewin Boehnke, Sergej Brener, Emanuel Gull, Václav Janiš, Christoph Jung, Martin Kecker, Gabriel Kotliar, Gang Li, Andrew Millis, Hartmut Monien, Alexander Poteryaev, Michael Potthoff, Leonid Pourovskii, Matouš Ringel and Philipp Werner.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hartmut Hafermann
    • 1
  • Frank Lechermann
    • 2
  • Alexei N. Rubtsov
    • 3
  • Mikhail I. Katsnelson
    • 4
  • Antoine Georges
    • 5
    • 6
  • Alexander I. Lichtenstein
    • 2
  1. 1.Centre de Physique Théorique CNRSÉcole PolytechniquePalaiseau CedexFrance
  2. 2.I. Institut für Theoretische PhysikUniversität HamburgHamburgGermany
  3. 3.Department of PhysicsMoscow State UniversityMoscowRussia
  4. 4.Institute for Molecules and MaterialsRadboud University NijmegenNijmegenThe Netherlands
  5. 5.Centre de Physique Théorique, CNRSÉcole PolytechniquePalaiseau CedexFrance
  6. 6.Collège de FranceParisFrance

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