Here, we calculate the bipartite R enyi entanglement entropy of an L x L x 2 bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. 111, 130402 (2013)]. Two types of bipartition are studied: (i) One that divides the lattice into two L x L planes, and (ii) One that divides the lattice into two equal-size (L x L=2 x 2) bilayers. Furthermore, we compare our calculations with those for the tight-binding model studied by the correlation matrix method. As expected, the entropy for bipartition (i) scales as L

^{2}, while the latter scales with L with possible logarithmic corrections. The onset of the antiferromagnet to singlet transition shows up by a saturation of the former to a maximal value and the latter to a small value in the singlet phase. We also comment on the large uncertainties in the numerical results with increasing U, which would have to be overcome before the critical behavior and logarithmic corrections can be quanti ed.- Publication Date:

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

- Type:
- Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 15; Journal ID: ISSN 1098-0121

- Publisher:
- American Physical Society (APS)

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

- Sponsoring Org:
- USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

- Country of Publication:
- United States

- Language:
- English

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

- OSTI Identifier:
- 1344113

- Alternate Identifier(s):
- OSTI ID: 1181167

```
Chang, Chia-Chen, Singh, Rajiv R. P., and Scalettar, Richard T..
```*Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices*. United States: N. p.,
Web. doi:10.1103/PhysRevB.90.155113.

```
Chang, Chia-Chen, Singh, Rajiv R. P., & Scalettar, Richard T..
```*Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices*. United States. doi:10.1103/PhysRevB.90.155113.

```
Chang, Chia-Chen, Singh, Rajiv R. P., and Scalettar, Richard T.. 2014.
"Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices". United States.
doi:10.1103/PhysRevB.90.155113. https://www.osti.gov/servlets/purl/1344113.
```

```
@article{osti_1344113,
```

title = {Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices},

author = {Chang, Chia-Chen and Singh, Rajiv R. P. and Scalettar, Richard T.},

abstractNote = {Here, we calculate the bipartite R enyi entanglement entropy of an L x L x 2 bilayer Hubbard model using a determinantal quantum Monte Carlo method recently proposed by Grover [Phys. Rev. Lett. 111, 130402 (2013)]. Two types of bipartition are studied: (i) One that divides the lattice into two L x L planes, and (ii) One that divides the lattice into two equal-size (L x L=2 x 2) bilayers. Furthermore, we compare our calculations with those for the tight-binding model studied by the correlation matrix method. As expected, the entropy for bipartition (i) scales as L2, while the latter scales with L with possible logarithmic corrections. The onset of the antiferromagnet to singlet transition shows up by a saturation of the former to a maximal value and the latter to a small value in the singlet phase. We also comment on the large uncertainties in the numerical results with increasing U, which would have to be overcome before the critical behavior and logarithmic corrections can be quanti ed.},

doi = {10.1103/PhysRevB.90.155113},

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

number = 15,

volume = 90,

place = {United States},

year = {2014},

month = {10}

}