Thermodynamically consistent description of criticality in models of correlated electrons

Abstract

Criticality in models of correlated electrons emerges in proximity of a low-temperature singularity in a two-particle Green function. Such singularities are generally related to a symmetry breaking of the one-particle self-energy. A consistent description demands that the symmetry breaking in the self-energy emerges at the critical point of the respective two-particle function. This cannot easily be achieved in models of correlated electrons, since there are two ways connecting one- and two-electron functions that cannot be made fully equivalent in approximations. We present a general construction of diagrammatic two-particle approximations consistent with the one-particle functions so that both produce qualitatively the same quantum critical behavior in thermodynamically equivalent descriptions. The general scheme is applied on the single-impurity Anderson model to derive qualitatively the same Kondo critical scale from the spectral function and the magnetic susceptibility.

15 pages, 10 figures

References in corpus (7)

• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
• A finite-frequency functional RG approach to the single impurity Anderson model
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
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Cited by in corpus (25)

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• Parquet-like equations for the Hedin three-leg vertex
• Conservation in two-particle self-consistent extensions of dynamical-mean-field-theory
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model
• Parquet approximation for molecules: spectrum and optical conductivity of the Pariser-Parr-Pople model
• Competition between antiferromagnetic and charge density wave fluctuations in the extended Hubbard model
• Mean-field approximation for thermodynamic and spectral functions of correlated electrons: Strong-coupling and arbitrary band filling
• Local correlation functions of arbitrary order for the Falicov-Kimball model
• Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency
• Single impurity Anderson model out of equilibrium: A two-particle semi-analytic approach
• Curie-Weiss susceptibility in strongly correlated electron systems
• Many-body perturbation theory for the superconducting quantum dot: Fundamental role of the magnetic field
• 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
• A functional-analysis derivation of the parquet equation
• The plain and simple parquet approximation: single- and multi-boson exchange in the two-dimensional Hubbard model