Strong-coupling approach to the Mott--Hubbard insulator on a Bethe lattice in Dynamical Mean-Field Theory

TL;DR

This paper analytically calculates the Hubbard bands of the half-filled Hubbard model on a Bethe lattice using a strong-coupling perturbation approach within Dynamical Mean-Field Theory, showing good agreement with numerical results.

Contribution

It introduces an analytical method to compute Hubbard bands in the strong-coupling regime using Kato--Takahashi perturbation theory within DMFT, including third-order corrections.

Findings

Hubbard band gaps match DDMRG results near the transition

Density of states agrees well with numerical data

Secondary Hubbard sub-bands are accurately captured

Abstract

We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato--Takahashi perturbation theory to solve the self-consistency equation of the Dynamical Mean-Field Theory analytically for the single-impurity Anderson model in multi-chain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Even close to the Mott--Hubbard transition, our results for the Mott--Hubbard gap agree very well with those from numerical Dynamical Density-Matrix Renormalization Group (DDMRG) calculations. The density of states of the lower Hubbard band also agrees very well with DDMRG data, apart from a resonance contribution at the upper band edge which cannot be reproduced in low-order perturbation theory.