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

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.

Authors:
 [1];  [2];  [3]
  1. ORNL
  2. University of Cincinnati
  3. University of California, Santa Barbara
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Center for Nanophase Materials Sciences; Center for Computational Sciences
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1003569
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review B; Journal Volume: 74; Journal Issue: 9
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; APPROXIMATIONS; BRILLOUIN ZONES; EIGENFUNCTIONS; EIGENVALUES; FREQUENCY DEPENDENCE; HUBBARD MODEL; PAIRING INTERACTIONS

Citation Formats

Maier, Thomas A, Jarrell, Mark, and Scalapino, Douglas. Pairing Interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum Monte Carlo approximation. United States: N. p., 2006. Web. doi:10.1103/PhysRevB.74.094513.
Maier, Thomas A, Jarrell, Mark, & Scalapino, Douglas. Pairing Interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum Monte Carlo approximation. United States. doi:10.1103/PhysRevB.74.094513.
Maier, Thomas A, Jarrell, Mark, and Scalapino, Douglas. Sun . "Pairing Interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum Monte Carlo approximation". United States. doi:10.1103/PhysRevB.74.094513.
@article{osti_1003569,
title = {Pairing Interaction in the two-dimensional Hubbard model studied with a dynamic cluster quantum Monte Carlo approximation},
author = {Maier, Thomas A and Jarrell, Mark and Scalapino, Douglas},
abstractNote = {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.},
doi = {10.1103/PhysRevB.74.094513},
journal = {Physical Review B},
number = 9,
volume = 74,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 2006},
month = {Sun Jan 01 00:00:00 EST 2006}
}