Numerical Evidence of Luttinger and Fermi liquid behavior in the 2D-Hubbard Model

The two dimensional Hubbard model with a single spin-up electron interacting with a finite density of spin-down electrons is studied using the quantum Monte Carlo technique, a new conjugate gradient method for the evaluation of the Edwards wavefunction ansatz, and the standard second order perturbation theory. We performed simulations up to 242 sites at U/t = 4 reaching the zero temperature properties with no “fermion sign problem” and found a surprisingly good accuracy of the Edwards wavefunction ansatz at low density or low doping. The conjugate gradient method was then applied to system up to 1922 sites and infinite U for the Edwards state. Fermi liquid theory seems to remain stable in 2D for all cases studied with the exception of the half filling case where a “Luttinger like behavior” survives in the Hubbard model , yielding a vanishing quasiparticle weight in the thermodynamic limit. Typeset using REVTEX