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

Sandro Sorella
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Abstract

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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Sandro Sorella. 1993-08-02. Numerical Evidence of Luttinger and Fermi Liquid Behaviour in the 2D Hubbard Model. https://doi.org/10.1103/physrevb.49.12373

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