Structure of the Pairing Interaction in the Two-Dimensional Hubbard Model

Abstract

Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for $d_{x^2-y^2}$ pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the $Q=(\pi ,\pi )$ spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin $S=1$ exchange channel.