HUBBARD-MODEL WITH UNCONSTRAINED HOPPING ON A FINITE NUMBER OF SITES

The simplified version of the Hubbard model, obtained by allowing hoppings between all pairs of sites, is studied for a finite number L of lattice sites, by using the theory of representations of the symmetric group S(L). The secular problem splits into sets of equations where each set refers to a different representation of S(L). The dimension of the secular problem is enormously reduced. Analytic expressions are found for the eigenvalues E+/- corresponding to the identical representation and it is conjectured that E+ is the highest eigenvalue. Some previous results of van Dongen and Vollhardt on the thermodynamic limit of the model are confirmed and the limit for large U is briefly discussed.