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 chemical potential m . This allows us to investigate the dependence of the leading Fermi-liquid dependencies on the band structure as the Fermi surface evolves from a circle at m ;24t to a square at m50. The form of the single-particle self-energy S(pW ,E) is determined by the densitydensity correlation function x(qW ,v) which develops two peaks for m*22.5t unlike the parabolic band case. Near half-filling, x(qW ,v) becomes independent of v , one-dimensional behavior, at intermediate values of v , which leads to the one-dimensional behavior in S(pW ,E). However, with m<20.1t there is no influence on the Fermi-liquid dependencies from the spin-density wave instability. We find that throughout the doping region S(pW ,E) remains qualitatively the same as for the isotropic Fermi surface with quantitative differences. The strong pW and E dependence of the off-shell self-energy S(p ,E) found earlier for the parabolic band is recovered for m&2t but deviates from this develop for m*20.1t . The resonance peak width of the spectral function A(pW E), has a linear dependence in jpW due to the E dependence of the imaginary part of S(pW ,E). We point out that an accurate detailed form for S(pW ,E) would be very difficult 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 Hubbard model carry over to Hamiltonians with finite range interactions.