Metal-insulator transition in an Hubbard-like model with degeneracy in one dimension

We consider the SU(N) generalization of the one-dimensional Hubbard model with arbitrary degeneracy N (spin and orbital degrees of freedom). This model is integrable and has several unusual properties at low temperatures. The Bethe-Ansatz equations at T=0 are analyzed in the thermodynamic limit in the absence of external fields. In the continuum limit, the effective interaction between the charge degrees of freedom corresponds to a potential of the form [sinh(ax)]^-2, where x is the distance between the particles involved and a is an inverse length scale. In the limit N{→}{∞} and in the continuum limit, the charges reduce to a Bose gas interacting via a {δ}-function potential. We further address here the properties of the charge degrees of freedom for a band filling close to one electron per site. The charge excitations obey Fermi statistics. We find a Mott metal-insulator transition at a critical value Uc of the Coulomb repulsion. Uc depends on N (Uc=0 for N=2). A qualitative change in the charge-rapidity distribution is found at Uc. The Fermi velocity is finite for UUc, diverges as U{→}Uc, and vanishes for U>Uc.