Low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction: Density-matrix renormalization-group calculations and perturbation theory

We investigate low-energy excitations of the one-dimensional half-filled SU(4) Hubbard model with an attractive on-site interaction $U<0$ using the density-matrix renormalization-group method as well as perturbation theory. We find that the ground state is a charge-density-wave state with long-range order. The ground state is completely incompressible since all the excitations are gapful. The charge gap, which is the same as the four-particle excitation gap, is a nonmonotonic function of $U$, while the spin gap and others increase with increasing $\mid U\mid$ and have linear asymptotic behaviors.

Figure 1

Ground-state energy correction per site from ${\mathcal{H}}_{\mathrm{eff}}^{\left(2\right)}$ (solid line) versus $U$ in comparison with DMRG data (엯).

Figure 2

DMRG results for charge gap (+) and four-particle gap (엯) versus $U$ in comparison with perturbation results (solid line). Error bars are smaller than size of symbols except for ${\Delta }_c$ at $U=-1$, as estimated by keeping different states.

Figure 3

DMRG results for one particle gap ${\Delta }_1$ (×), two-particle gap ${\Delta }_2$ (◻), spin gap ${\Delta }_s$ (▵), four-particle excitation gap ${\Delta }_4$ (엯), and charge gap ${\Delta }_c$ (+) are shown as a function of $U$. The results of HF RPA calculations, for ${\Delta }_1$, ${\Delta }_2$, and ${\Delta }_s$ are denoted by solid, dot-dashed, and dashed lines, respectively. Inset shows $\Delta ∕\mid U\mid$ versus $U$ for ${\Delta }_1$ (×), ${\Delta }_2$ (◻), and ${\Delta }_s$ (▵).