Densities of states of the Falicov-Kimball model off half filling in infinite dimensions

TL;DR

This paper develops an approximate analytical scheme within DMFT to study the densities of states in the Falicov-Kimball model away from half filling, revealing spectral features and phase separation effects.

Contribution

It introduces a new approximation method within DMFT for the asymmetric Hubbard model and applies it to the Falicov-Kimball model off half filling, providing insights into spectral functions.

Findings

Spectra of localized particles vary with particle concentration and temperature.

Phase separation influences the spectral function significantly.

Approximate results align with known exact solutions in limiting cases.

Abstract

An approximate analytical scheme of the dynamical mean field theory (DMFT) is developed for the description of the electron (ion) lattice systems with Hubbard correlations within the asymmetric Hubbard model where the chemical potentials and electron transfer parameters depend on an electron spin (a sort of ions). Considering a complexity of the problem we test the approximation in the limiting case of the infinite-$U$ spinless Falicov-Kimball model. Despite the fact that the Falicov-Kimball model can be solved exactly within DMFT, the densities of states of localized particles have not been completely investigated off half filling. We use the approximation to obtain the spectra of localized particles for various particle concentrations (chemical potentials) and temperatures. The effect of a phase separation phenomenon on the spectral function is considered.