Mean-field approximation for thermodynamic and spectral functions of correlated electrons: Strong-coupling and arbitrary band filling

Abstract

We present a construction of a mean-field theory for thermodynamic and spectral properties of correlated electrons reliable in the strong-coupling limit. We introduce an effective interaction determined self-consistently from the reduced parquet equations. It is a static local approximation of the two-particle irreducible vertex, the kernel of a potentially singular Bethe-Salpeter equation. The effective interaction enters the Ward identity from which a thermodynamic self-energy, renormalizing the one-electron propagators, is determined. The dynamical Schwinger-Dyson equation with the thermodynamic propagators is then used to calculate the spectral properties. The thermodynamic and spectral properties of correlated electrons are in this way determined on the same footing and in a consistent manner. Such a mean-field approximation is analytically controllable and free of unphysical behavior and spurious phase transitions. We apply the construction to the asymmetric Anderson impurity and the Hubbard models in the strong-coupling regime.

13 pages, 11 figures

References in corpus (5)

• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Analytic impurity solver with the Kondo strong-coupling asymptotics
• Thermodynamically consistent description of criticality in models of correlated electrons

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• Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic field
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• Curie-Weiss susceptibility in strongly correlated electron systems
• Spin correlations in the bilayer Hubbard model with perpendicular electric field
• Failure of the mean-field description of magnetic fluctuations in the superconducting quantum dot
• Failure of the Baym-Kadanoff construction to match consistently quantum dynamics with thermodynamic critical behavior
• Antiferromagnetic fluctuations in the one-dimensional Hubbard model