The Mott transition in the strong coupling perturbation theory

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→0U→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 0UcU>Uc the Mott gap disappears.