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.
Ehsan Khatami, A. Macridin, and M. Jarrell. "Validity of the spin-susceptibility “glue” approximation for pairing in the two-dimensional Hubbard model" Physical Review B (2009). doi:10.1103/PhysRevB.80.172505