Insulating charge density wave for a half-filled SU(N) Hubbard model with an attractive on-site interaction in one dimension

TL;DR

This paper investigates a one-dimensional SU(N) Hubbard model with attractive interactions at half-filling, revealing a charge density wave insulator with a degenerate ground state and gapped excitations, contrasting with the SU(2) case.

Contribution

It provides a detailed analysis of the insulating charge density wave state in the SU(N) Hubbard model with attractive interactions, including excitation gaps and their dependence on coupling strength.

Findings

Ground state is a degenerate charge density wave insulator.

All excitations are gapped, leading to insulating behavior.

Charge gap equals the Cooperon gap, with specific dependence on N, U, and t.

Abstract

We study a one-dimensional SU(N) Hubbard model with an attractive on-site interaction and $N>2$ at half-filling on the bipartite lattice using density-matrix renormalization-group method and a perturbation theory. We find that the ground state of the SU(N) Hubbard model is a charge density wave state with two-fold degeneracy. All the excitations are found to be gapful, resulting in an insulating ground state, on contrary to that in the SU(2) case. Moreover, the charge gap is equal to the Cooperon gap, which behaves as $-2Nt^2/(N-1)U$ in the strong coupling regime. However, the spin gap $\Delta_{s}$ and the quasiparticle gap $\Delta_{1}$ as well open exponentially in the weak coupling region, while in the strong coupling region, they linearly depend on $U$ such that $\Delta_{s}\sim -U(N-1)$ and $\Delta_{1}\sim -U(N-1)/2$.