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Strong Electronic Correlations: Dynamical Mean-Field Theory and Beyond

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Modern Theories of Many-Particle Systems in Condensed Matter Physics

Part of the book series: Lecture Notes in Physics ((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.

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Notes

  1. 1.

    In the notation of Sect. 4.2 N should then be replaced the number of clusters \(N/N_{\rm{c}}\) and the momentum \({{\mathbf{k}}}\) should be identified with the superlattice momentum \(\tilde{\user2{k}}.\)

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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.

Author information

Authors and Affiliations

  1. Centre de Physique Théorique CNRS, École Polytechnique, 91128, Palaiseau Cedex, France

    Hartmut Hafermann

  2. I. Institut für Theoretische Physik, Universität Hamburg, 20355, Hamburg, Germany

    Frank Lechermann & Alexander I. Lichtenstein

  3. Department of Physics, Moscow State University, 119992, Moscow, Russia

    Alexei N. Rubtsov

  4. Institute for Molecules and Materials, Radboud University Nijmegen, Nijmegen, 6525 AJ, The Netherlands

    Mikhail I. Katsnelson

  5. Centre de Physique Théorique, CNRS, École Polytechnique, 91128, Palaiseau Cedex, France

    Antoine Georges

  6. Collège de France, 11 place Marcellin Berthelot, 75005, Paris, France

    Antoine Georges

Authors
  1. Hartmut Hafermann
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  2. Frank Lechermann
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  3. Alexei N. Rubtsov
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  4. Mikhail I. Katsnelson
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  5. Antoine Georges
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  6. Alexander I. Lichtenstein
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Corresponding author

Correspondence to Hartmut Hafermann .

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Editors and Affiliations

  1. , Departamento de Física/IFLP, Universidad Nacional de La Plata, La Plata, 1900, Argentina

    Daniel C. Cabra

  2. , Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, Göttingen, 37077, Germany

    Andreas Honecker

  3. , Laboratoire de Physique Théorique, Université Paul Sabatier, Route de Narbonne 118, Toulouse Cedex 4, 31062, France

    Pierre Pujol

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© 2012 Springer-Verlag Berlin Heidelberg

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Hafermann, H., Lechermann, F., Rubtsov, A.N., Katsnelson, M.I., Georges, A., Lichtenstein, A.I. (2012). Strong Electronic Correlations: Dynamical Mean-Field Theory and Beyond. In: Cabra, D., Honecker, A., Pujol, P. (eds) Modern Theories of Many-Particle Systems in Condensed Matter Physics. Lecture Notes in Physics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10449-7_4

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  • DOI: https://doi.org/10.1007/978-3-642-10449-7_4

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