# 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:

- ORNL
- University of Cincinnati
- 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}

}