Abstract
A dynamic cluster quantum Monte Carlo approximation is used to study the
effective pairing interaction of a 2D Hubbard model with a near neighbor
hopping $t$ and an on-site Coulomb interaction $U$ . The effective
pairing interaction is characterized in terms of the momentum and
frequency dependence of the eigenfunction of the leading eigenvalue of
the irreducible particle-particle vertex. The momentum dependence of
this eigenfunction is found to vary as $(\cos k_x-\cos k_y)$ over most
of the Brillouin zone and its frequency dependence is determined by the
$S=1$ particle-hole continuum which for large $U$ varies as several
times $J$. This implies that the effective pairing interaction is
attractive for singlets formed between near-neighbor sites and retarded
on a time scale set by $(2J)^{-1}$. The strength of the pairing
interaction measured by the size of the d-wave eigenvalue peaks for $U$
of order the bandwidth $8t$. It is found to increase as the system is
underdoped.
