# Determinant quantum Monte Carlo study of $d$ -wave pairing in the plaquette Hubbard hamiltonian

## Abstract

We used the determinant Quantum Monte Carlo (DQMC) to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters - a two-dimensional square lattice consisting of elemental 2x2 plaquettes with hopping t and on-site repulsion U coupled by an interplaquette hopping t' ≤ t. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half-filling by the inhomogeneous hopping or not. For U/t = 4, DQMC indicates an optimal t'/t ≈ 0.4 at which the pairing vertex is most attractive. We also found that optimal t'/t increases with U/t. We then contrast our results for this plaquette model with a Hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three band CuO _{2} model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.

- Authors:

- Harbin Inst. of Technology (China). Dept. of Physics
- Pennsylvania State Univ., University Park, PA (United States). Physics Dept.; Univ. of California, Davis, CA (United States). Physics Dept.
- Federal Univ. of Rio de Janeiro (Brazil). Inst. of Physics
- Univ. of California, Davis, CA (United States). Physics Dept.

- Publication Date:

- Research Org.:
- Univ. of California, Davis, CA (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1344108

- Alternate Identifier(s):
- OSTI ID: 1180226

- Grant/Contract Number:
- NA0001842; NA0001842-0

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics

- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 7; Journal ID: ISSN 1098-0121

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Ying, T., Mondaini, R., Sun, X. D., Paiva, T., Fye, R. M., and Scalettar, R. T.
```*Determinant quantum Monte Carlo study of d -wave pairing in the plaquette Hubbard hamiltonian*. United States: N. p., 2014.
Web. doi:10.1103/PhysRevB.90.075121.

```
Ying, T., Mondaini, R., Sun, X. D., Paiva, T., Fye, R. M., & Scalettar, R. T.
```*Determinant quantum Monte Carlo study of d -wave pairing in the plaquette Hubbard hamiltonian*. United States. doi:10.1103/PhysRevB.90.075121.

```
Ying, T., Mondaini, R., Sun, X. D., Paiva, T., Fye, R. M., and Scalettar, R. T. Wed .
"Determinant quantum Monte Carlo study of d -wave pairing in the plaquette Hubbard hamiltonian". United States.
doi:10.1103/PhysRevB.90.075121. https://www.osti.gov/servlets/purl/1344108.
```

```
@article{osti_1344108,
```

title = {Determinant quantum Monte Carlo study of d -wave pairing in the plaquette Hubbard hamiltonian},

author = {Ying, T. and Mondaini, R. and Sun, X. D. and Paiva, T. and Fye, R. M. and Scalettar, R. T.},

abstractNote = {We used the determinant Quantum Monte Carlo (DQMC) to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters - a two-dimensional square lattice consisting of elemental 2x2 plaquettes with hopping t and on-site repulsion U coupled by an interplaquette hopping t' ≤ t. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half-filling by the inhomogeneous hopping or not. For U/t = 4, DQMC indicates an optimal t'/t ≈ 0.4 at which the pairing vertex is most attractive. We also found that optimal t'/t increases with U/t. We then contrast our results for this plaquette model with a Hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three band CuO2 model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.},

doi = {10.1103/PhysRevB.90.075121},

journal = {Physical Review. B, Condensed Matter and Materials Physics},

number = 7,

volume = 90,

place = {United States},

year = {Wed Aug 13 00:00:00 EDT 2014},

month = {Wed Aug 13 00:00:00 EDT 2014}

}

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