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

Abstract

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)${]}^{\mathrm{\ensuremath{-}}2}$, where x is the distance between the particles involved and a is an inverse length scale. In the limit N\ensuremath{\rightarrow}\ensuremath{\infty} and in the continuum limit, the charges reduce to a Bose gas interacting via a \ensuremath{\delta}-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 ${\mathit{U}}_{\mathit{c}}$ of the Coulomb repulsion. ${\mathit{U}}_{\mathit{c}}$ depends on N (${\mathit{U}}_{\mathit{c}}$=0 for N=2). A qualitative change in the charge-rapidity distribution is found at ${\mathit{U}}_{\mathit{c}}$. The Fermi velocity is finite for U${\mathit{U}}_{\mathit{c}}$, diverges as U\ensuremath{\rightarrow}${\mathit{U}}_{\mathit{c}}$, and vanishes for U>${\mathit{U}}_{\mathit{c}}$.