Towards analytic description of a transition from weak to strong coupling regime in correlated electron systems. I. Systematic diagrammatic theory with two-particle Green functions

Abstract

We analyze behavior of correlated electrons described by Hubbard-like models at intermediate and strong coupling. We show that with increasing interaction a pole in a generic two-particle Green function is approached. The pole signals metal-insulator transition at half filling and gives rise to a new vanishing ``Kondo'' scale causing breakdown of weak-coupling perturbation theory. To describe the critical behavior at the metal-insulator transition a novel, self-consistent diagrammatic technique with two-particle Green functions is developed. The theory is based on the linked-cluster expansion for the thermodynamic potential with electron-electron interaction as propagator. Parquet diagrams with a generating functional are derived. Numerical instabilities due to the metal-insulator transition are demonstrated on simplifications of the parquet algebra with ring and ladder series only. A stable numerical solution in the critical region is reached by factorization of singular terms via a low-frequency expansion in the vertex function. We stress the necessity for dynamical vertex renormalizations, missing in the simple approximations, in order to describe the critical, strong-coupling behavior correctly. We propose a simplification of the full parquet approximation by keeping only most divergent terms in the asymptotic strong-coupling region. A qualitatively new, feasible approximation suitable for the description of a transition from weak to strong coupling is obtained.

17 pages, 4 figures, REVTeX

References in corpus (2)

• Metal-insulator transition and magnetic ordering in Hubbard models near the Nagaoka limit
• Linked Cluster Expansion Around Mean-Field Theories of Interacting Electrons

Cited by in corpus (19)

• Local Electronic Correlation at the Two-Particle Level
• On the fulfillment of Ward identities in the functional renormalization group approach
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Dynamical vertex approximation in its parquet implementation: application to Hubbard nano-rings
• Parquet decomposition calculations of the electronic self-energy
• Anomalous self-energy and Fermi surface quasi-splitting in the vicinity of a ferromagnetic instability
• Thermodynamically consistent description of criticality in models of correlated electrons
• The two-loop functional renormalization-group approach to the one- and two-dimensional Hubbard model
• On the separability of dynamical and non-local correlations in three dimensions
• Mean-field approximation for thermodynamic and spectral functions of correlated electrons: Strong-coupling and arbitrary band filling
• Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency
• Complementary views on electron spectra: From Fluctuation Diagnostics to real space correlations
• Curie-Weiss susceptibility in strongly correlated electron systems
• Single impurity Anderson model out of equilibrium: A two-particle semi-analytic approach
• Development of an efficient impurity solver in dynamical mean field theory for multi-band systems: The iterative perturbation theory combined with the parquet equations
• Two-particle renormalizations in many-fermion perturbation theory: Importance of the Ward identity
• Simplification of the local full vertex in the impurity problem in DMFT and its applications for the nonlocal correlation
• Failure of the Baym-Kadanoff construction to match consistently quantum dynamics with thermodynamic critical behavior
• Improvement of the simplification method for the local two-particle full-vertex towards precise frequency behavior