Conservation in two-particle self-consistent extensions of dynamical mean-field theory

Friedrich Krien, Erik G.C.P. Van Loon, Hartmut Hafermann, Junya Otsuki, Mikhail I. Katsnelson, Alexander I. Lichtenstein

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


Extensions of dynamical mean-field theory (DMFT) make use of quantum impurity models as nonperturbative and exactly solvable reference systems which are essential to treat the strong electronic correlations. Through the introduction of retarded interactions on the impurity, these approximations can be made two-particle self-consistent. This is of interest for the Hubbard model because it allows to suppress the antiferromagnetic phase transition in two dimensions in accordance with the Mermin-Wagner theorem, and to include the effects of bosonic fluctuations. For a physically sound description of the latter, the approximation should be conserving. In this paper, we show that the mutual requirements of two-particle self-consistency and conservation lead to fundamental problems. For an approximation that is two-particle self-consistent in the charge and longitudinal spin channels, the double occupancy of the lattice and the impurity is no longer consistent when computed from single-particle properties. For the case of self-consistency in the charge and longitudinal as well as transversal spin channels, these requirements are even mutually exclusive so that no conserving approximation can exist. We illustrate these findings for a two-particle self-consistent and conserving DMFT approximation.

Original languageEnglish
Article number075155
JournalPhysical Review B
Issue number7
Publication statusPublished - Aug 24 2017
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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