Quantum Monte Carlo simulations of Hubbard type models

Abstract

We present a review of recent Quantum Monte-Carlo results for one- and twodimensional Hubbard models. In one-dimension spectral properties are calculated with the maximum entropy method. At small doping, the one-particle excitations are characterized by a dispersive cosine-like band. Two different velocities for charge and spin-excitations are obtained which lead to a conformal charge c = 0.98 ± 0.05. In two-dimensions, we concentrate on two methods to detect superconducting ground states without prior knowledge of the symmetry of the underlying pair-pair correlations: flux quantization and the temperature derivative of the superfluid density. Both methods are based on extensions of quantum Monte-Carlo algorithms to incorporate magnetic fields. Our main results include numerical data which a) confirm the Kosterlitz-Thouless transition in the attractive Hubbard model b) show the absence of superconductivity in the quarter filled repulsive Hubbard model, and finally c) show no sign of a Kosterlitz-Thouless type transition in the three-band Hubbard model up to βtpd = 12.5 and hole doping δ = 0.25.