Quantum Monte Carlo Study of Hole Binding and Pairing Correlations in the Three-Band Hubbard Model

TL;DR

This study uses the Constrained Path Monte Carlo method to investigate hole pairing and superconductivity in the three-band Hubbard model, revealing hole binding but rapid decay of pairing correlations with distance.

Contribution

It provides the first large-scale simulation of the three-band Hubbard model showing hole binding and analyzing pairing correlations with system size and interaction strength.

Findings

Holes bind over a range of parameters and binding increases with system size.

Pairing correlation functions decay quickly with distance.

Long-range correlations are suppressed as Coulomb interaction increases.

Abstract

We simulated the 3-band Hubbard model using the Constrained Path Monte Carlo (CPMC) method in search for a possible superconducting ground state. The CPMC is a ground state method which is free of the exponential scaling of computing time with system size. We calculated the binding energy of a pair of holes for systems up to $6 \times 4$ unit cells. We also studied the pairing correlation functions versus distance for both the d-wave and extended s-wave channels in systems up to $6 \times 6$. We found that holes bind for a wide range of parameters and that the binding increased as the system size is increased. However, the pairing correlation functions decay quickly with distance. For the extended s channel, we found that as the Coulomb interaction $U_d$ on the Cu sites is increased, the long-range part of the correlation functions is suppressed and fluctuates around zero. For the $d_{x^2 - y^2}$ channel, we found that the correlations decay rapidly with distance towards a small positive value. However, this value becomes smaller as the interaction $U_d$ or the system size is increased.