Validity of the spin-susceptibility "glue" approximation for pairing in the two-dimensional Hubbard model

TL;DR

This study evaluates the weak coupling spin-susceptibility 'glue' approximation's effectiveness in modeling pairing in the 2D Hubbard model for cuprates, comparing it with the more accurate dynamical cluster approximation.

Contribution

The paper demonstrates that the SSGA fails to reproduce the leading pairing symmetries of the DCA and shows that improvements with added d-wave terms are dominated by these additional contributions.

Findings

SSGA does not capture the leading pairing symmetries of DCA.

Adding a d-wave term to SSGA results in a stronger contribution than the original 'glue' approximation.

The 'glue' approximation's limitations are evident in realistic model parameters.

Abstract

We examine the validity of the weak coupling spin-susceptibility "glue" approximation (SSGA) in a two-dimensional Hubbard model for cuprates. For comparison, we employ the well-established dynamical cluster approximation (DCA) with a quantum Monte Carlo algorithm as a cluster solver. We compare the leading eigenvalues and corresponding eigenfunctions of the DCA and SSGA pairing matrices. For realistic model parameters, we find that the SSGA fails to capture the leading pairing symmetries seen in the DCA. Furthermore, when the SSGA is improved through the addition of a term with d-wave symmetry, the strength of this additional term is found to be larger than that of the "glue" approximation.