Order parameter symmetries for magnetic and superconducting instabilities: Bethe-Salpeter analysis of functional renormalization-group solutions

TL;DR

This paper combines the Bethe-Salpeter equation with the functional renormalization group to analyze order parameter symmetries in the 2D t-t' Hubbard model, revealing complex deviations from simple forms due to frustration and competing interactions.

Contribution

It introduces a novel combined approach to study order parameter structures, uncovering complex symmetries and competition effects in the Hubbard model.

Findings

Deviations from pure s-, d-, p-wave forms due to frustration.

Extended s-wave in particle-hole channel with antiferromagnetic coupling.

Competition between ferromagnetism and triplet pairing near t' = 1/2.

Abstract

The Bethe-Salpeter equation is combined with the temperature-cutoff functional renormalization group approach to analyze the order parameter structure for the leading instabilities of the 2D t-t' Hubbard model. We find significant deviations from pure s-, d-, or p-wave forms, which is due to the frustration of antiferromagnetism at small and intermediate t'. With adding a direct antiferromagnetic spin-exchange coupling the eigenfunctions in the particle-hole channel have extended s-wave form, while in the particle-particle singlet pairing channel a higher angular momentum component arises besides the standard d-wave symmetry, which flattens the angular dependence of the gap. For t' closer to 1/2 we find a delicate competition of ferromagnetism and triplet pairing with a nontrivial pair-wavefunction.