Analytic Treatment of Mott-Hubbard Transition in the Half-Filled Hubbard Model

TL;DR

This paper analytically investigates the Mott-Hubbard transition in the half-filled Hubbard model, revealing the nature of the transition and its characteristics in different states, with results consistent with infinite-dimensional limits.

Contribution

It provides an analytical approach to the Mott-Hubbard transition, including Green's function calculations and insights into the transition's order and spectral features.

Findings

Transition is second order at the ground state.

Hubbard bands collapse at transition point.

Results recover infinite-dimensional behavior.

Abstract

The Mott-Hubbard transition in the half-filled Hubbard model is studied analytically for the paramagnetic ground state and the classical N\'{e}el state. The single-particle density of states is obtained by calculating the Green's function represented by the infinite continued fraction. The paramagnetic solution shows that the Mott-Hubbard transition is signaled by both collapsing Hubbard bands and appearing $\delta$-function peak at midgap, and the transition is second order at the ground state. We also provide specific heats in metallic regime to demonstrate that our results recover those of infinite dimension.