METALLIC STATES IN THE HUBBARD-MODEL AT HALF-FILLING

Using second-order perturbation theory in U for the self-energy, we solve the self-consistent equations for the local Green function of the infinite-dimensional Hubbard model. We consider the cases of Gaussian and semicircular free densities of states (DOS), and calculate the spectral densities rho(omega) for various U. In the semicircular case we investigate the existence of a Mon transition at half-filling. Even for large U we obtain a metallic solution. Treating the free Dos as a variable parameter, the method also gives an approximate solution of the finite-dimensional Hubbard model. We consider the case of a (regularized) logarithmic Dos appropriate for the two-dimensional case.