THE HUBBARD-MODEL - FROM SMALL TO LARGE-U

The Hubbard model is investigated starting from both the small and large U limits. This allows one to derive an interpolation formula for the double occupancy at half-filling for dimensionalities d = 1, 2, 3. It shows a smooth behavior as a function of U and tends to zero only for U --> infinity. A quantity that probes more sensitivity the nature of the ground state is the momentum distribution function n(k). At half filling n(k) is smooth at k(F) both for d = 1 and d = 2, at least for not too small values of U. In one dimension for all other band fillings the slope of n(k) has a power-law singularity at k(F) with an exponent alpha increasing steadily from zero at U = 0 to 1/8 for U --> infinity; the system is a "marginal Fermi liquid". A similar behavior may occur close to half-filling for d = 2, but for small densities one expects the usual step function of a normal Fermi liquid.