Evolution of Fermi-liquid behavior with doping in the Hubbard model: Influence of the band structure

We calculate the single-particle Green's function for a contact interaction with nearest-neighbor hopping on a square lattice as a function of chemica l potential mu. This allows us to investigate the dependence of the leading Fermi-liquid dependencies on the band structure as the Fermi surface evolv es from a circle at mu similar to -4t to a square at mu=0. The form of the single-particle self-energy Sigma((p) over bar,E) is determined by the dens ity-density correlation function chi((q) over right arrow,omega) which deve lops two peaks for mu greater than or similar to-2.5t unlike the parabolic band case. Near half-filling, chi((q) over right arrow,omega) becomes indep endent of omega, one-dimensional behavior, at intermediate values of omega, which leads to the one-dimensional behavior in Sigma((p) over right arrow, E). However, with mu less than or equal to-0.1t there is no influence on th e Fermi-liquid dependencies from the spin-density wave instability. We find that throughout the doping region Sigma((p) over right arrow,E) remains qu alitatively the same as for the isotropic Fermi surface with quantitative d ifferences. The strong p and E dependence of the off-shell self-energy B(p, E) found earlier for the parabolic band is recovered for mu less than or si milar to-t but deviates from this develop for mu greater than or similar to -0.1t. The resonance peak width of the spectral function A ((p) over right arrow E), has a linear dependence in xi(p)(-) due to the E dependence of th e imaginary part of Sigma((p) over right arrow, E). We point out that an ac curate detailed form for Sigma((p) over right arrow,E) would be very diffic ult to recover from angle-resolved photoemission spectroscopy data for the spectral density. Since the leading corrections are determined by the long wavelength particle-hole excitations, the results found here for the Hubbar d model carry over to Hamiltonians with finite range interactions.