Mott transition and dimerization in the one-dimensional SU$(n)$ Hubbard model

TL;DR

This study uses DMRG to analyze the SU(n) Hubbard model in 1D, revealing universal gapped phases and dimerization at half filling, with a Kosterlitz-Thouless transition at zero interaction strength.

Contribution

It provides the first detailed numerical analysis of the SU(n) Hubbard model for multiple n values, uncovering the nature of the Mott transition and dimerization phenomena.

Findings

Finite spin and charge gaps for n>2 at half filling.

Transition is of Kosterlitz-Thouless type at U=0.

Dimerization occurs in the gapped phase for all n.

Abstract

The one-dimensional SU$(n)$ Hubbard model is investigated numerically for $n=2,3,4$, and 5 at half filling and $1/n$ filling using the density-matrix renormalization-group (DMRG) method. The energy gaps and various quantum information entropies are calculated. In the half-filled case, finite spin and charge gaps are found for arbitrary positive $U$ if $n > 2$. Furthermore, it is shown that the transition to the gapped phase at $U_{\rm c}=0$ is of Kosterlitz-Thouless type and is accompanied by a bond dimerization both for even and odd $n$. In the $1/n$-filled case, the transition has similar features as the metal-insulator transition in the half-filled SU(2) Hubbard model. The charge gap opens exponentially slowly for $U>U_{\rm c}=0$, the spin sector remains gapless, and the ground state is non-dimerized.