Equation of motion approach to the Hubbard model in infinite dimensions

TL;DR

This paper develops a systematic series of self-consistent approximations for the Hubbard model's Green's function in infinite dimensions, analyzing the Mott-Hubbard transition with increasing approximation order.

Contribution

It introduces a new method based on equations of motion to improve approximations for the Hubbard model in infinite dimensions, including the Hubbard-III approximation as a special case.

Findings

Analytic and numerical results for the Mott-Hubbard transition at half filling.

Higher-order approximations provide more accurate descriptions of the transition.

The approach systematically improves upon existing approximations.

Abstract

We consider the Hubbard model on the infinite-dimensional Bethe lattice and construct a systematic series of self-consistent approximations to the one-particle Green's function, $G^{(n)}(\omega),\ n=2,3,\dots\ $ . The first $n-1$ equations of motion are exactly fullfilled by $G^{(n)}(\omega)$ and the $n$'th equation of motion is decoupled following a simple set of decoupling rules. $G^{(2)}(\omega)$ corresponds to the Hubbard-III approximation. We present analytic and numerical results for the Mott-Hubbard transition at half filling for $n=2,3,4$.