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

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.