Enhanced pair-correlation functions in the two-dimensional Hubbard model

TL;DR

This paper uses a novel quantum Monte Carlo method to compute pair correlation functions in the 2D Hubbard model, revealing size-dependent enhancement of d-wave pairing correlations away from half-filling, suggesting possible superconductivity.

Contribution

It introduces a new diagonalization algorithm in quantum Monte Carlo that avoids the negative sign problem and demonstrates size-dependent pairing correlation enhancement.

Findings

Enhanced d-wave pairing correlations for U>0 when doping away from half-filling.

Pair correlation function increases with system size, indicating potential superconductivity.

No pairing enhancement at half-filling, implying no superconductivity without doping.

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 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 P_d is increased for U>0 compared to the non-interacting case, while P_d is suppressed for U>0 when the system size is small. The enhancement ratio P_d[U]/P_d[U=0] will give a criterion on the existence of superconductivity. The ratio P_d[U]/P_d[U=0] increases almost linearly \propto L as the system size L\times L is increased. This increase is a good indication of an existence of superconducting phase in the two-dimensional Hubbard model. There is, however, no enhancement of pair correlation functions at half-filling, which indicates the absence of superconductivity without hole doping.