Green's functions of infinite-U asymmetric Hubbard model: Falicov-Kimball limit

TL;DR

This paper develops an analytical approach using Green's functions to study the infinite-U asymmetric Hubbard model in the Falicov-Kimball limit, analyzing phase transitions and particle densities.

Contribution

It introduces an approximate analytical method based on irreducible Green's functions for the asymmetric Hubbard model in the Falicov-Kimball limit, with comparisons to exact thermodynamic results.

Findings

Calculated chemical potential dependence on concentration.

Obtained densities of states for localized particles.

Analyzed phase transitions across thermodynamic regimes.

Abstract

The asymmetric Hubbard model is used in investigating the lattice gas of the moving particles of two types. The model is considered within the dynamical mean-field method. The effective single-site problem is formulated in terms of the auxiliary Fermi-field. To solve the problem an approximate analytical method based on the irreducible Green's function technique is used. This approach is tested on the Falicov-Kimball limit (when the mobility of ions of either type is infinitesimally small) of the infinite-U case of the model considered. The dependence of chemical potentials on concentration is calculated using the one-particle Green's functions, and different approximations are compared with the exact results obtained thermodynamically. The densities of states of localized particles are obtained for different temperatures and particle concentrations. The phase transitions are investigated for the case of the Falicov-Kimball limit in different thermodynamic regimes.