Tracing the Mott-Hubbard transition in one-dimensional Hubbard models without Umklapp scattering

TL;DR

This paper uses DMRG to study the Mott-Hubbard transition in a one-dimensional Hubbard model without Umklapp scattering, accurately determining the critical interaction and gap behavior analytically and numerically.

Contribution

It provides a precise numerical analysis of the Mott-Hubbard transition in a simplified 1D model, highlighting the role of the slope of the momentum distribution at band edges.

Findings

Critical interaction strength U_c=W where the gap opens linearly

The momentum distribution slope at band edges signals the transition

Single-particle bound state formation indicates the transition point

Abstract

We apply the density-matrix renormalization group (DMRG) method to a one-dimensional Hubbard model that lacks Umklapp scattering and thus provides an ideal case to study the Mott-Hubbard transition analytically and numerically. The model has a linear dispersion and displays a metal-to-insulator transition when the Hubbard interaction~$U$ equals the band width, $U_{\rm c}=W$, where the single-particle gap opens linearly, $\Delta(U\geq W)=U-W$. The simple nature of the elementary excitations permits to determine numerically with high accuracy the critical interaction strength and the gap function in the thermodynamic limit. The jump discontinuity of the momentum distribution $n_k$ at the Fermi wave number $k_{\rm F}=0$ cannot be used to locate accurately $U_{\rm c}$ from finite-size systems. However, the slope of $n_k$ at the band edges, $k_{\rm B}=\pm \pi$, reveals the formation of a single-particle bound state which can be used to determine $U_{\rm c}$ reliably from $n_k$ using accurate finite-size data.