The Mott transition in the strong coupling perturbation theory

TL;DR

This paper derives a self-consistent equation for the electron Green's function in the Hubbard model using strong coupling perturbation theory, accurately describing the Mott transition and its dependence on interaction strength.

Contribution

It introduces a new self-consistent equation within strong coupling perturbation theory that captures the Mott transition and aligns with known approximations like Hubbard-III.

Findings

The Mott transition occurs at U_c = sqrt(3) * Delta / 2.

The derived equation retains causality and matches known limits.

The density of states shifts and redistributes with doping and interaction strength.

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 $\Delta$ 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.