Evolution of Fermi Liquid Behavior with Doping in the Hubbard Model
Abstract
Description
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.
Revtex, 31 pages with 17 figures, Submitted to PRB
Revtex, 31 pages with 17 figures, Submitted to PRB