Enhanced pair correlation functions in the two-dimensional Hubbard model

Abstract

In this study we have computed the pair correlation functions in the two-dimensional Hubbard model using a quantum Monte Carlo method. We employ a new diagonalization algorithm in the quantum Monte Carlo method which is free from the negative sign problem. We show that the d-wave pairing correlation function is indeed enhanced slightly for the positive on-site Coulomb interaction U when doping away from the half-filling. When the system size becomes large, the pair correlation function Pd increases for U > 0 compared to the non-interacting case, while Pd is suppressed for U > 0 when the system size is small. The enhancement ratio Pd[U]/Pd[U = 0] will give a criterion on the existence of superconductivity. The ratio Pd[U]/Pd[U = 0] increases almost linearly ∝L when the system size L × L is increased. This increase is a good indication of the existence of a superconducting phase in the two-dimensional Hubbard model. There is, however, no enhancement of pair correlation functions in the half-filled case, which indicates the absence of superconductivity without hole doping.