Evolution of the spectrum and the metal-insulator transition in local approximations for many-electron models

TL;DR

This paper investigates how the electron spectrum evolves and the metal-insulator transition occurs in many-electron models using local approximations, highlighting the effects of various interactions and the spectrum's structure.

Contribution

It introduces a self-consistent approach within local approximations to analyze the spectrum evolution and metal-insulator transition, connecting with CPA and DMFT methods.

Findings

Reproduction of three-peak structure of the density of states near the transition

Analysis of factors influencing the shape of the density of states

Use of locator representation to avoid non-analyticities in Green's functions

Abstract

In the framework of the many-electron s-d exchange model and Hubbard model, self-consistent equations are derived for the one-particle retarded Green's function in the many-electron Hubbard X-operator representation. We analyze the general structure of the single-site approximations and their connection with the coherent potential approximation (CPA) and dynamic effective field theory (DMFT). Using the self-consistent approximation, we examine in detail the picture of the evolution of the electron spectrum with the model parameters (coupling constants, the concentration of charge carriers). The influence of various factors (Kondo many-electron scattering, smearing due to damping, dynamics of localized moment subsystem) on the shape of the density of states N(E) in the interacting system is investigated. It is shown that the use of the locator representation allows to avoid in some cases the non-analyticity in approximate expressions for the Green's functions. Our approach enables one to reproduce, at certain values of the parameters, three-peak structure of N(E) near the metal-insulator transition.