Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency

Abstract

A two-particle self-consistency is rarely part of mean-field theories. It is, however, essential for avoiding spurious critical transitions and unphysical behavior. We present a general scheme for constructing analytically controllable approximations with self-consistent equations for the two-particle vertices based on the parquet equations. We explain in detail how to reduce the full set of parquet equations not to miss quantum criticality in strong coupling. We further introduce a decoupling of convolutions of the dynamical variables in the Bethe-Salpeter equations to make them analytically solvable. We connect the self-energy with the two-particle vertices to satisfy the Ward identity and the Schwinger-Dyson equation. We discuss the role of the one-particle self-consistency in making the approximations reliable in the whole spectrum of the input parameters. We demonstrate the general construction on the simplest static approximation that we apply to the Kondo behavior of the single-impurity Anderson model.

arXiv comment16 pages, 14 figures

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Cited by in corpus (10)

• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Rigorous Wilsonian Renormalization Group for impurity models with a spectral gap
• Unified theory of quantum phase transitions in quantum dots with gapped host bands
• Curie-Weiss susceptibility in strongly correlated electron systems
• Single impurity Anderson model out of equilibrium: A two-particle semi-analytic approach
• Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic 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
• Kondo Temperature and High to Low Temperature Crossover in Quantum Dots