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 -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 U₂ of the Coulomb repulsion. U₂ depends on N (U₂=0 for N=2). A qualitative change in the charge-rapidity distribution is found at U₂. The Fermi velocity is finite for UU₂, diverges as UU₂, and vanishes for U>U₂.