Dynamical Density-Matrix Renormalization Group for the Mott--Hubbard insulator in high dimensions

TL;DR

This paper employs a high-resolution dynamical density-matrix renormalization group method within dynamical mean-field theory to accurately study the Mott insulator transition in the Hubbard model on a Bethe lattice, revealing detailed spectral features.

Contribution

It introduces a systematic fixed-energy DMFT approach combined with DDMRG to achieve superior spectral resolution in studying the Mott transition.

Findings

The Mott gap closes at a critical interaction strength Uc/t=4.45.

High-resolution density of states reveals shoulders near Hubbard band edges.

Quasi-particle resonance splits at the transition point.

Abstract

We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth $W=4t$ at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling $U_{\rm c}/t=4.45 \pm 0.05$. At $U=4.5t$, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at $U_{\rm c}$.