Analytical and Numerical Treatment of the Mott--Hubbard Insulator in Infinite Dimensions

TL;DR

This paper combines analytical calculations and a new numerical scheme to study the Mott--Hubbard insulator in infinite dimensions, revealing the gap opening at a critical interaction strength and characterizing the density of states near the gap.

Contribution

It introduces a novel 'Fixed-Energy Exact Diagonalization' method for DMFT and provides analytical insights into the density of states and gap formation in the Hubbard model.

Findings

Gap opens at Uc=4.43 ± 0.05

Density of states near the gap increases as frequency^{1/2}

New numerical scheme corroborated by other approaches

Abstract

We calculate the density of states in the half-filled Hubbard model on a Bethe lattice with infinite connectivity. Based on our analytical results to second order in $t/U$, we propose a new `Fixed-Energy Exact Diagonalization' scheme for the numerical study of the Dynamical Mean-Field Theory. Corroborated by results from the Random Dispersion Approximation, we find that the gap opens at $U_{\rm c}=4.43 \pm 0.05$. Moreover, the density of states near the gap increases algebraically as a function of frequency with an exponent $\alpha=1/2$ in the insulating phase. We critically examine other analytical and numerical approaches and specify their merits and limitations when applied to the Mott--Hubbard insulator.