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

TL;DR

This study uses advanced numerical methods to investigate the 2D Hubbard model, providing evidence that Fermi liquid behavior persists except at half-filling where Luttinger-like behavior emerges, indicating non-Fermi liquid properties.

Contribution

The paper introduces a combination of quantum Monte Carlo, a new conjugate gradient method, and perturbation theory to analyze the 2D Hubbard model at large system sizes and low temperatures.

Findings

Fermi liquid behavior remains stable in 2D for most cases.

Luttinger-like behavior appears at half-filling with vanishing quasiparticle weight.

Accurate simulations up to 242 sites and 1922 sites were achieved.

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.