Attractive and repulsive pairing interaction vertices for the two-dimensional Hubbard model

Particle-hole-magnetic and particle-particle-pairing susceptibilities can be expressed in terms of dressed Green's functions and interaction vertices. Using quantum Monte Carlo simulation techniques, the effect of the interaction vertices is examined to determine the sign and relative magnitude of the effective pairing interaction in various channels for the two-dimensional Hubbard model. Near half filling we find that the singlet $d_{x^2-y^2}$ pairing interaction is the most attractive. The extended near-neighbor $s$ interaction is also weakly attractive, while the singlet $s_{\mathrm{xy}}$ and $d_{\mathrm{xy}}$ and the triplet $p_x$ interactions are repulsive.