Kato, Kohtaro and Brandão, Fernando G. S. L. (2020) Toy model of boundary states with spurious topological entanglement entropy. Physical Review Research, 2 (3). Art. No. 032005. ISSN 2643-1564. doi:10.1103/physrevresearch.2.032005. https://resolver.caltech.edu/CaltechAUTHORS:20200707-115529620
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Abstract
Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminate topological entanglement entropy. We show that, if the state at the boundary of a subregion is a stabilizer state, then it has a nonzero spurious contribution to the region if and only if the state is in a nontrivial one-dimensional G₁×G₂ symmetry-protected-topological (SPT) phase under an on-site symmetry. However, we provide a candidate of a boundary state that has a nonzero spurious contribution but does not belong to any such SPT phase.
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| Additional Information: | © 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 21 February 2020; revised 27 April 2020; accepted 29 April 2020; published 7 July 2020. K.K. thanks Arpit Dua for a discussion about stacking 1D models to construct a 2D model. K.K. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907). F.B. is supported by the NSF. The numerical calculation in this paper was implemented in the Caltech HPC center. | |||||||||
| Group: | Institute for Quantum Information and Matter | |||||||||
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| Issue or Number: | 3 | |||||||||
| DOI: | 10.1103/physrevresearch.2.032005 | |||||||||
| Record Number: | CaltechAUTHORS:20200707-115529620 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200707-115529620 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 104255 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 07 Jul 2020 19:13 | |||||||||
| Last Modified: | 16 Nov 2021 18:29 |
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