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The Pseudoparticle Approach to Strongly Correlated Electron Systems

  • Raymond FrésardEmail author
  • Johann Kroha
  • Peter Wölfle
Chapter
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 171)

Abstract

The most prominent pseudoparticle representations and their applications to correlated spin and electronic models are reviewed, with approximate solution schemes ranging from saddle-point approximations with Gaussian fluctuations to conserving approximations and renormalization group (RG) techniques. Merits and shortcomings of these methods are described. In particular, the generic feature of radial slave boson fields to possess a finite expectation value is discussed, while pure fluctuation fields may best be treated by conserving approximations. We present applications to the magnetic phases of the Anderson lattice model and to the Hubbard model. The noncrossing approximation and the conserving T-matrix approximation are presented and discussed as the most important conserving approximations. Furthermore RG techniques for pseudoparticle representations, including “poor man’s scaling” and functional RG for the Kondo model in and out of equilibrium, a novel RG approach to the Kondo model for strong coupling, and the functional RG approach to frustrated Heisenberg models are discussed.

Keywords

Renormalization Group Hubbard Model Functional Renormalization Group Auxiliary Particle Renormalization Group Flow 
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 thank Jan Brinckmann, Theo Costi, Klaus Doll, Michael Dzierzawa, Peter Hirschfeld, Stefan Kirchner, Thilo Kopp, Gabi Kotliar, Burkhard Möller, Kandkher Muttalib, Andrzej Oleś, Henni Ouerdane, Jens Paaske, Marcin Raczkowski, Johannes Reuther, Achim Rosch, Holger Schmidt, and Walter Zimmermann for valuable collaboration. RF gratefully acknowledges financial support by the Région Basse-Normandie and the Ministère de la Recherche. JK is grateful for financial support from the Deutsche Forschungsgemeinschaft through SFB 608 and through grant No. KR 1727/1-2 and PW acknowledges support through the DFG Research Center for Functional Nanostructures (CFN) and the DFG Research Unit 960 “Quantum Phase Transitions”.

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Authors and Affiliations

  1. 1.Laboratoire CrismatUMR CNRS-ENSICAEN(ISMRA) 6508Caen CEDEX 4France
  2. 2.Physikalisches InstitutUniversität BonnBonnGermany
  3. 3.Institut für Theorie der Kondensierten Materie and Institut für NanotechnologieKarlsruher Institut für Technologie (KIT)KarlsruheGermany

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