Toy model of boundary states with spurious topological entanglement entropy
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.032005 |
| _version_ | 1827286091302961152 |
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| author | Kohtaro Kato Fernando G. S. L. Brandão |
| author_facet | Kohtaro Kato Fernando G. S. L. Brandão |
| author_sort | Kohtaro Kato |
| collection | DOAJ |
| description | 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 G_{1}×G_{2} 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. |
| first_indexed | 2024-04-24T10:25:40Z |
| format | Article |
| id | doaj.art-2c358ced3a724b15b7745c68e2c18e40 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:25:40Z |
| publishDate | 2020-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-2c358ced3a724b15b7745c68e2c18e402024-04-12T16:56:39ZengAmerican Physical SocietyPhysical Review Research2643-15642020-07-012303200510.1103/PhysRevResearch.2.032005Toy model of boundary states with spurious topological entanglement entropyKohtaro KatoFernando G. S. L. BrandãoTopological 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 G_{1}×G_{2} 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.http://doi.org/10.1103/PhysRevResearch.2.032005 |
| spellingShingle | Kohtaro Kato Fernando G. S. L. Brandão Toy model of boundary states with spurious topological entanglement entropy Physical Review Research |
| title | Toy model of boundary states with spurious topological entanglement entropy |
| title_full | Toy model of boundary states with spurious topological entanglement entropy |
| title_fullStr | Toy model of boundary states with spurious topological entanglement entropy |
| title_full_unstemmed | Toy model of boundary states with spurious topological entanglement entropy |
| title_short | Toy model of boundary states with spurious topological entanglement entropy |
| title_sort | toy model of boundary states with spurious topological entanglement entropy |
| url | http://doi.org/10.1103/PhysRevResearch.2.032005 |
| work_keys_str_mv | AT kohtarokato toymodelofboundarystateswithspurioustopologicalentanglemententropy AT fernandogslbrandao toymodelofboundarystateswithspurioustopologicalentanglemententropy |