Strong coupling approach in dynamical mean-field theory for strongly correlated electron systems

TL;DR

This paper reviews two analytical methods within DMFT for strongly correlated electrons, using perturbation expansions and diagrammatic techniques to derive self-consistent equations and analyze electronic properties.

Contribution

It introduces two novel analytical approaches in DMFT based on perturbation theory and diagrammatic techniques, unifying and extending existing approximations.

Findings

Derived density of states for different approximations

Analyzed chemical potential and magnetic order parameters

Compared results of various self-consistent schemes

Abstract

We review two analytical approaches in Dynamical Mean-Field Theory (DMFT) based on a perturbation theory expansion over the electron hopping to and from the self consistent environment. In the first approach the effective single impurity Anderson model (SIAM) is formulated in terms of the auxiliary Fermi-fields and the projection (irreducible Green's function) technique is used for its solution. A system of the DMFT equations is obtained that includes as simple specific cases a number of known approximations (Hubbard-III, AA, MAA, ...). The second approach is based on the diagrammatic technique (Wick's theorem) for Hubbard operators that allows to construct a thermodynamically consistent theory when SIAM exactly splits into four components (subspaces): two Fermi liquid and two non-Fermi liquid. The results for the density of states, concentration dependences of the band energies, chemical potential and magnetic order parameters are presented for different self-consistent approximations (AA, strong coupling Hartree--Fock and further).