Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices
Abstract
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.
- Authors:
-
- Univ. of California, Davis, CA (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
- OSTI Identifier:
- 1344113
- Alternate Identifier(s):
- OSTI ID: 1181167
- Grant/Contract Number:
- NA0001842; NA0001842-0
- Resource 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)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
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., 2014.
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. https://doi.org/10.1103/PhysRevB.90.155113
Chang, Chia-Chen, Singh, Rajiv R. P., and Scalettar, Richard T. Fri .
"Entanglement properties of the antiferromagnetic-singlet transition in the Hubbard model on bilayer square lattices". United States. https://doi.org/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 = {Fri Oct 10 00:00:00 EDT 2014},
month = {Fri Oct 10 00:00:00 EDT 2014}
}
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