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
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- 1.
We are grateful to T.A. Costi for providing the NRG data.
- 2.
Note, however, that CTMA includes all potential scattering terms up to O(Γ 4).
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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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Frésard, R., Kroha, J., Wölfle, P. (2012). The Pseudoparticle Approach to Strongly Correlated Electron Systems. In: Avella, A., Mancini, F. (eds) Strongly Correlated Systems. Springer Series in Solid-State Sciences, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21831-6_3
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