Quantum Monte Carlo study of the pairing symmetry competition in the Hubbard model

TL;DR

This study uses quantum Monte Carlo methods to explore pairing symmetries in Hubbard models relevant to unconventional superconductors, revealing dominant triplet f-wave pairing in quasi-1D systems and competing interactions in 2D systems.

Contribution

It provides a detailed comparison of singlet and triplet pairing channels in Hubbard models, highlighting the conditions favoring different pairing symmetries.

Findings

Triplet f-wave pairing dominates in quasi-1D Hubbard model.

d-wave pairing interaction is stronger than triplet in 2D Hubbard model.

Triplet pairing interactions are attractive but less dominant in 2D systems.

Abstract

To shed light into the pairing mechanism of possible spin-triplet superconductors (TMTSF)$_2$X and Sr$_2$RuO$_4$, we study the competition among various spin singlet and triplet pairing channels in the Hubbard model by calculating the pairing interaction vertex using the ground state quantum Monte Carlo technique. We model (TMTSF)$_2$X by a quarter-filled quasi-one dimensional (quasi-1D) Hubbard model,and the $\gamma$ band of Sr$_2$RuO$_4$ by a two dimensional (2D) Hubbard model with a band filling of $\sim 4/3$. For the quasi-1D system, we find that triplet $f$-wave pairing not only dominates over triplet p-wave in agreement with the spin fluctuation theory, but also looks unexpectedly competitive against d-wave. For the 2D system, although the results suggest presence of attractive interaction in the triplet pairing channels, the d-wave pairing interaction is found to be larger than those of the triplet channels.