Mott transition in the asymmetric Hubbard model at half-filling within dynamical mean-field theory

We apply the approximate analytic methods to the investigation of the band structure of the asymmetric Hubbard model where the chemical potentials and electron transfer parameters depend on the electron spin (type of quasiparticles). The Hubbard-I and alloy-analogy approximations are the simplest approximations which are used. Within the alloy-analogy approximation, the energy band of particles does not depend on the transfer parameter of particles of another sort. It means that the gap in the spectrum opens at the critical value $U_{c}$ that is the same in two different limiting cases: the Falicov-Kimball model and the standard Hubbard model. The approximate analytic scheme of the dynamical mean-field theory is developed to include into the theory the scattering of particles responsible for the additional mechanism (due to the transfer of particles of another sort) of the band formation. We use the so-called GH3 approach that is a generalization of the Hubbard-III approximation. The approach describes the continuous Mott transition with the $U_{c}$ value dependent on a ratio of transfer parameters of different particles.Comment: 10 pages, 10 figure

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

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.Comment: 9 pages, 11 figures, submitted to Phys. Rev.