Metal-insulator transition in the one-dimensional SU(N) Hubbard model

TL;DR

This paper studies the metal-insulator transition in the one-dimensional SU(N) Hubbard model, combining bosonization theory with advanced quantum Monte Carlo simulations to identify the critical interaction strength for the transition.

Contribution

It provides new theoretical predictions and highly accurate numerical results for the critical Coulomb interaction in the SU(N) Hubbard model for N=3 and 4.

Findings

Identification of the Mott transition at finite U for N=3 and 4

Quantitative estimates of critical U: ~2.2 for N=3 and ~2.8 for N=4

Validation of theoretical predictions with improved Monte Carlo methods

Abstract

We investigate the metal-insulator transition of the one-dimensional SU(N) Hubbard model for repulsive interaction. Using the bosonization approach a Mott transition in the charge sector at half-filling (k_F=\pi/Na_0) is conjectured for N > 2. Expressions for the charge and spin velocities as well as for the Luttinger liquid parameters and some correlation functions are given. The theoretical predictions are compared with numerical results obtained with an improved zero-temperature quantum Monte Carlo approach. The method used is a generalized Green's function Monte Carlo scheme in which the stochastic time evolution is partially integrated out. Very accurate results for the gaps, velocities, and Luttinger liquid parameters as a function of the Coulomb interaction U are given for the cases N=3 and N=4. Our results strongly support the existence of a Mott-Hubbard transition at a {\it non-zero} value of the Coulomb interaction. We find $U_c \sim 2.2$ for N=3 and $U_c \sim 2.8$ for N=4.