Strong-coupling approach for strongly correlated electron systems

TL;DR

This paper develops a diagrammatic perturbation theory for strongly correlated electron systems based on Hubbard operators, providing analytical insights into the Hubbard model's thermodynamics and electronic structure in different doping regimes.

Contribution

It introduces a novel diagrammatic scheme using Hubbard operators and derives analytical results for the Hubbard model in infinite dimensions, capturing Fermi-liquid and non-Fermi-liquid behaviors.

Findings

Analytical solutions for Green's functions with two- and four-pole structures.

Identification of Fermi-liquid and non-Fermi-liquid contributions depending on doping.

Thermodynamically consistent approach in the infinite-dimensional limit.

Abstract

A perturbation theory scheme in terms of electron hopping, which is based on the Wick theorem for Hubbard operators, is developed. Diagrammatic series contain single-site vertices connected by hopping lines and it is shown that for each vertex the problem splits into the subspaces with ``vacuum states'' determined by the diagonal Hubbard operators and only excitations around these vacuum states are allowed. The rules to construct diagrams are proposed. In the limit of infinite spatial dimensions the total auxiliary single-site problem exactly splits into subspaces that allows to build an analytical thermodynamically consistent approach for a Hubbard model. Some analytical results are given for the simple approximations when the two-pole (alloy-analogy solution) and four-pole (Hartree-Fock approximation) structure for Green's function is obtained. Two poles describe contribution from the Fermi-liquid component, which is dominant for small electron and hole concentrations (``overdoped case'' of high-$T_c$'s), whereas other two describe contribution from the non-Fermi liquid and are dominant close to half-filling (``underdoped case'').