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 → ∞. A quantity that probes more sensitively the nature of the ground state is the momentum distribution function n(k). At half filling n(k) is smooth at kF 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 kF with an exponent α increasing steadily from zero at U = 0 to 1/8 for U → ∞; 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.