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 $\Delta$ 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 gives the correct result in the limit $U\rightarrow 0$. Calculations were performed for the semi-elliptical initial band. It is shown that the approximation describes the Mott transition, which occurs at $U_c=\sqrt{3}\Delta/2$. This value coincides with that obtained in the Hubbard-III approximation. 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 $U>U_c$ the Mott gap disappears.