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

TL;DR

This paper develops an approximate analytical approach within dynamical mean-field theory to study the Mott transition in the asymmetric Hubbard model, revealing how transfer parameters influence the critical interaction strength.

Contribution

It introduces a generalized Hubbard-III based scheme to analyze the continuous Mott transition considering asymmetric transfer parameters.

Findings

The energy gap opens at a critical U_c similar to the Falicov-Kimball and Hubbard models.

The critical U_c depends on the ratio of transfer parameters of different particles.

The approach captures the continuous nature of the Mott transition.

Abstract

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.