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arXiv:cond-mat/0509240 · The European Physical Journal B

Fermionic renormalization group flow into phases with broken discrete symmetry: charge-density wave mean-field model

Roland Gersch, Carsten Honerkamp A, D. Rohe, Walter Metzner

Published Dec 1, 2005• 40 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2005-00416-8

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We extend the functional renormalization group technique in a modi cation of the one‐particle irreducible scheme to study discrete symmetry breaking at nite temperature. As an instructive example, we employ the technique to access both the symmetric and the symmetry‐broken phase of a charge‐density wave mean‐ eld model. We study the half‐ lled case, and thus the breaking of a discrete symmetry, at nite temperature. A small external symmetry‐breaking eld allows us to access the symmetry‐broken state without encountering any divergence in the o w. We show diagrammatically that our method is equivalent to an exact resummation treatment. We numerically study the dependence of the o w on the external eld and on temperature.

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First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here, we introduce a counterterm technique within the functional renormalization-group (fRG) formalism which allows access to all stable and metastable configurations. It becomes possible to study symmetry-broken states which occur through first-order transitions as well as hysteresis phenomena. For continuous transitions, the standard results are reproduced. As an example, we study discrete-symmetry breaking in a mean-field model for a commensurate charge-density wave. An additional benefit of the approach is that away from the critical temperature for the breaking of discrete symmetries large interactions can be avoided at all RG scales.
First-order phase transitions in many-fermion systems are not detected\n in the susceptibility analysis of common renormalization-group (RG)\n approaches. Here, we introduce a counterterm technique within the\n functional renormalization-group (fRG) formalism which allows access to\n all stable and metastable configurations. It becomes possible to study\n symmetry-broken states which occur through first-order transitions as\n well as hysteresis phenomena. For continuous transitions, the standard\n results are reproduced. As an example, we study discrete-symmetry\n breaking in a mean-field model for a commensurate charge-density wave.\n An additional benefit of the approach is that away from the critical\n temperature for the breaking of discrete symmetries large interactions\n can be avoided at all RG scales.
We extend the functional renormalization group technique in a modi cation of the one‐particle irreducible scheme to study discrete symmetry breaking at nite temperature. As an instructive example, we employ the technique to access both the symmetric and the symmetry‐broken phase of a charge‐density wave mean‐ eld model. We study the half‐ lled case, and thus the breaking of a discrete symmetry, at nite temperature. A small external symmetry‐breaking eld allows us to access the symmetry‐broken state without encountering any divergence in the o w. We show diagrammatically that our method is equivalent to an exact resummation treatment. We numerically study the dependence of the o w on the external eld and on temperature.