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

Details 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 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

1997-04-09

arxiv.org/abs/cond-mat/9704076v1

J. Phys.: Condens. Matter 10, 2915 (1998)

Physics

Condensed Matter

Strongly Correlated Electrons

17 pages, 4 figures, REVTeX

Scientific paper

10.1088/0953-8984/10/13/010

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.

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