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

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 $\Delta_{1}\sim -U(N-1)/2$.