Metal-insulator transition with infinite-range Coulomb coupling: Fractional statistics and quantum critical properties

We show that the Hubbard model with infinite-range Coulomb coupling is equi valent to an ideal gas of three species of particles obeying fractional exc lusion statistics. A full appreciation of this mapping requires an extensio n of the pertinent formalism. This very simple, but rather peculiar model i s exactly solvable in any dimension and exhibits a Mott metal-insulator tra nsition, whose universality class is shown to be that of a free spinless Fe rmi gas. A modified version of the Luttinger theorem is shown to apply in a ny dimension. We also characterize the metallic and insulating phases by ob taining the electronic band structure as well as the interacting density of states. The fractional statistics manifests itself on the amplitudes of se veral thermodynamic quantities and, in particular, the Pauli spin susceptib ility is subdominant in all metallic phases, and a Curie-type of response a ppears.