The Mott transition in the strong coupling perturbation theory

Abstract

Using the strong coupling diagram technique a self-consistent equation for the electron Green׳s function is derived for the repulsive Hubbard model. Terms of two lowest orders of the ratio of the bandwidth Δ to the Hubbard repulsion U are taken into account in the irreducible part of the Larkin equation. The obtained equation is shown to retain causality and reduces to Green׳s function of uncorrelated electrons in the limit U→0. Calculations were performed for the semi-elliptical initial band. It is shown that the approximation describes the Mott transition, which occurs at Uc=3Δ/2. This value coincides with that obtained in the Hubbard-III approximation. At half-filling, for 0<U<Uc the imaginary part of the self-energy is nonzero at the Fermi level, which indicates that the obtained solution is not a Fermi liquid. At small deviations from half-filling the density of states shifts along the frequency axis without perceptible changes in its shape. For larger deviations the density of states is modified: it is redistributed in favor of the subband, in which the Fermi level is located, and for U>Uc the Mott gap disappears.