Evolution of Fermi Liquid Behavior with Doping in the Hubbard Model

Abstract

We calculate the single-particle Green's function for the tight-binding band structure, $ξ_{\vec p}=-2t\cos p_x-2t\cos p_y -μ$, with a function of chemical potential $μ$ for square-lattice system. The form of the single-particle self-energy, $Σ({\vec p}, E)$, is determined by the density-density correlation function, $χ({\vec q}, ω)$, which develops two peaks for $μ\gtrsim -2.5t$ unlike parabolic band case. Near half filling $χ({\vec q}, ω)$ becomes independent of $ω$, one dimensional behavior, at intermediate values of $ω$ which leads to one dimensional behavior in $Σ({\vec p},E)$. However $μ\leq -0.1t$ there is no influence on the Fermi Liquid dependences from SDW instability. The strong $\vec p$ and $E$ dependence of the off-shell self-energy, $Σ(p,E)$, found earlier for the parabolic band is recovered for $μ\lesssim -t$ but deviations from this develop for $μ\gtrsim -0.1t$. The resonance peak width of the spectral function, $A({\vec p}, E)$ has linear dependence in $ξ_{\vec p}$ due to the $E$ dependence of the imaginary part of $Σ({\vec p}, E)$. We point out that an accurate detailed form for $Σ({\vec p},E)$ would be very difficult to recover from ARPES data for the spectral density.