Spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model

We will discuss recent dynamic cluster quantum Monte Carlo studies of the effective pairing interaction responsible for d-wave pairing in the doped two-dimensional Hubbard model with an on-site Coulomb interaction U equal to the bandwidth. Motivated by earlier studies that show that the dominant contribution to the pairing interaction comes from the spin S=1 channel, we study a simple spin susceptibility representation of the particle-particle irreducible vertex. We find that with an effective temperature dependent coupling $\bar{U}(T)$ and the numerically calculated spin susceptibility $\chi(K-K')$, the d-wave pairing interaction is well approximated by $\frac{3}{2}\bar{U}^2(T) \chi(K-K')$.