Pairing interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum Monte Carlo approximation

A dynamic cluster quantum Monte Carlo approximation is used to study the effective pairing interaction of a two-dimensional Hubbard model with a near neighbor hopping t and an onsite 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 of the bandwidth 8t. It is found to increase as the system is underdoped.