Metal-insulator transition in the one-dimensional $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ Hubbard model

We investigate the metal-insulator transition of the one-dimensional $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ 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 $N>\mathrm{}2.\mathrm{}$ 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 $N=3\mathrm{}$ and $N=4.\mathrm{}$ Our results strongly support the existence of a Mott-Hubbard transition at a nonzero value of the Coulomb interaction. We find $U_c\sim 2.2$ for $N=3\mathrm{}$ and $U_c\sim 2.8$ for $N=4.\mathrm{}$