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

In terms of the Shubin-Vonsovskii many-electron s-d exchange model and Hubbard model, self-consistent equations for the one-particle retarded Green's function are derived in the representation of many-electron Hubbard X operators using the method of decoupling of chains of equations of motion. An analysis is given of the general structure of single-site approximations and of their relation to the coherent-potential approximation (CPA) and the dynamic mean-field theory (DMFT). Using the self-consistent approximations, the evolution of the electron spectrum upon the variation of the bare parameters of the model (coupling constants, charge-carrier concentrations) is investigated in detail. Effects of various factors (Kondo many-electrons scattering, damping-induced smearing, proper dynamics of the subsystem of localized momenta) on the shape of the density of states N(E) with allowance for interaction are discussed. It is shown that the use of the locator representation makes it possible in some cases to avoid nonanalyticities in the approximate expressions for the Green's functions. This approach permits the reproduction (at certain values of the parameters) of the three-peak structure of the DOS near the metal-insulator transition.