Numerical Evidence of Luttinger and Fermi Liquid Behaviour in the 2D Hubbard Model

Details Numerical Evidence of Luttinger and Fermi Liquid Behaviour in the 2D Hubbard Model Numerical Evidence of Luttinger and Fermi Liquid Behaviour in the 2D Hubbard Model

1993-08-02

arxiv.org/abs/cond-mat/9308001v1

Physics

Condensed Matter

10 pages + 4 pictures, RevTex, SISSA 121/93/CM/MB

Scientific paper

10.1103/PhysRevB.49.12373

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 Carlotechnique, 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.

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