Finite-temperature superconducting correlations of the Hubbard model

TL;DR

This study uses advanced numerical methods to analyze superconducting correlations in the Hubbard model, revealing tendencies towards d-wave pairing and demonstrating the effectiveness of NLCEs in exploring pairing phenomena at strong coupling.

Contribution

It applies NLCEs and quantum Monte Carlo to investigate pairing correlations, providing new insights into superconducting tendencies in the Hubbard model beyond magnetic and charge correlations.

Findings

Strong d-wave pairing tendency near half filling

Extended s-wave correlations saturate at low temperatures

NLCEs effectively probe pairing at strong coupling

Abstract

We utilize numerical linked-cluster expansions (NLCEs) and the determinantal quantum Monte Carlo algorithm to study pairing correlations in the square lattice Hubbard model. To benchmark the NLCE, we first locate the finite-temperature phase transition of the attractive model to a superconducting state away from half filling. We then explore the superconducting properties of the repulsive model for the d-wave and extended s-wave pairing symmetries. The pairing structure factor shows a strong tendency to d-wave pairing and peaks at an interaction strength comparable to the bandwidth. The extended s-wave structure factor and correlation length are larger at higher temperatures but clearly saturate as temperature is lowered, whereas the d-wave counterparts, which start off lower at high temperatures, continue to rise near half filling. This rise is even more dramatic in the d-wave susceptibility. The convergence of NLCEs breaks down as the susceptibilities and correlation lengths become large, so we are unable to determine the onset of long-range order. However, our results extend the conclusion, previously restricted to only magnetic and charge correlations, that NLCEs offer unique window into pairing in the Hubbard model at strong coupling.