Anomalous Fermi liquid effects in two-dimensional Hubbard model near half-filling

The Landau parameters F-0(s), F-0(a), F-1(s) and F-1(n) in the two-dimensional Hubbard model are calculated by the second order perturbation method of Abrikosov-Khalatatnikov. The following points are revealed as the half-filling is approached: (1) F-0(a) changes its sign from negative to positive, if the Coulomb interaction U is strong enough, i.e., U/t greater than or similar to 2.0. This means that, the spill density oscillations, zero spin-sound, can propagate there; (2) F-1(s) changes its sign from positive to negative, so that we can understand, on the basis of the anisotropic Fermi liquid theory, the behavior of the Drude weight whose magnitude decreases as the half-filling is approached even if there were no mass enhancement; (3) From the results of F-0(s) and F-0(a), it is shown that both the charge and spin susceptibility decrease rapidly close to the half-filling. The latter is regarded as the so-called spin-gap behavior.