The Pairing Interaction in the 2D Hubbard Model

T. A. Maier; M. Jarrell; D. J. Scalapino

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arXiv · cond-mat/0606003

The Pairing Interaction in the 2D Hubbard Model

T. A. Maier·M. Jarrell·D. J. Scalapino

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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 exchange energy $J$. This implies that the effective pairing interaction is attractive for singlets formed between near-neighbor sites and retarded on a time scale set by $J^{-1}$. 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.

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T. A. Maier, M. Jarrell, D. J. Scalapino. 2006-05-31. The Pairing Interaction in the 2D Hubbard Model. https://arxiv.org/abs/cond-mat/0606003

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