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

The simplified version of the Hubbard model, obtained by allowing hopp ings between all pairs of sites, is studied for a finite number L of l attice sites, by using the theory of representations of the symmetric group S(L). The secular problem splits into sets of equations where ea ch set refers to a different representation of S(L). The dimension of the secular problem is enormously reduced. Analytic expressions are fo und for the eigenvalues E+/- corresponding to the identical representa tion and it is conjectured that E+ is the highest eigenvalue. Some pre vious results of van Dongen and Vollhardt on the thermodynamic limit o f the model are confirmed and the limit for large U is briefly discuss ed.