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

Abstract

Using numerical dynamic cluster quantum Monte Carlo results, we study a simple approximation for the pairing interaction of a two-dimensional Hubbard model with an on-site Coulomb interaction $U$ equal to the bandwidth. We find that with an effective temperature-dependent coupling $\overline{U}(T)$ and the numerically calculated spin susceptibility $\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$, the $d$-wave pairing interaction is well approximated by $\frac{3}{2}{\overline{U}}^{2}\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$.