Mirror anomaly in fermionic topological orders
We study general 2D fermionic topological orders enriched by the mirror symmetry with M^{2}=1. It is known that certain mirror symmetry enriched fermionic topological orders (mirror SETs) are anomalous, in the sense that they cannot be realized in strict two dimensions but have to live on the surfac...
| Principais autores: | , |
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| Formato: | Artigo |
| Idioma: | English |
| Publicado em: |
American Physical Society
2020-06-01
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| coleção: | Physical Review Research |
| Acesso em linha: | http://doi.org/10.1103/PhysRevResearch.2.023339 |
| _version_ | 1827286112518799360 |
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| author | Bin-Bin Mao Chenjie Wang |
| author_facet | Bin-Bin Mao Chenjie Wang |
| author_sort | Bin-Bin Mao |
| collection | DOAJ |
| description | We study general 2D fermionic topological orders enriched by the mirror symmetry with M^{2}=1. It is known that certain mirror symmetry enriched fermionic topological orders (mirror SETs) are anomalous, in the sense that they cannot be realized in strict two dimensions but have to live on the surface of 3D topological crystalline superconductors. Mirror anomaly, or equivalently 3D topological crystalline superconductor, has a Z_{16} classification. In this work, we derive an explicit expression, namely, an anomaly indicator, for the Z_{16} mirror anomaly for general fermionic mirror SETs. This derivation is based on the recently developed folding approach, originally proposed for bosonic topological orders. We generalize it to fermion systems. Through this approach, we establish a direct bulk-boundary correspondence between surface fermionic topological orders and 3D bulk topological crystalline superconductors. In addition, during the derivation, we obtain some general properties of fermionic topological orders as well as a few constraints on the properties of fermionic mirror SETs. |
| first_indexed | 2024-04-24T10:26:01Z |
| format | Article |
| id | doaj.art-8081a54053364020aa7bddb78aa4ba52 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:26:01Z |
| publishDate | 2020-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-8081a54053364020aa7bddb78aa4ba522024-04-12T16:55:32ZengAmerican Physical SocietyPhysical Review Research2643-15642020-06-012202333910.1103/PhysRevResearch.2.023339Mirror anomaly in fermionic topological ordersBin-Bin MaoChenjie WangWe study general 2D fermionic topological orders enriched by the mirror symmetry with M^{2}=1. It is known that certain mirror symmetry enriched fermionic topological orders (mirror SETs) are anomalous, in the sense that they cannot be realized in strict two dimensions but have to live on the surface of 3D topological crystalline superconductors. Mirror anomaly, or equivalently 3D topological crystalline superconductor, has a Z_{16} classification. In this work, we derive an explicit expression, namely, an anomaly indicator, for the Z_{16} mirror anomaly for general fermionic mirror SETs. This derivation is based on the recently developed folding approach, originally proposed for bosonic topological orders. We generalize it to fermion systems. Through this approach, we establish a direct bulk-boundary correspondence between surface fermionic topological orders and 3D bulk topological crystalline superconductors. In addition, during the derivation, we obtain some general properties of fermionic topological orders as well as a few constraints on the properties of fermionic mirror SETs.http://doi.org/10.1103/PhysRevResearch.2.023339 |
| spellingShingle | Bin-Bin Mao Chenjie Wang Mirror anomaly in fermionic topological orders Physical Review Research |
| title | Mirror anomaly in fermionic topological orders |
| title_full | Mirror anomaly in fermionic topological orders |
| title_fullStr | Mirror anomaly in fermionic topological orders |
| title_full_unstemmed | Mirror anomaly in fermionic topological orders |
| title_short | Mirror anomaly in fermionic topological orders |
| title_sort | mirror anomaly in fermionic topological orders |
| url | http://doi.org/10.1103/PhysRevResearch.2.023339 |
| work_keys_str_mv | AT binbinmao mirroranomalyinfermionictopologicalorders AT chenjiewang mirroranomalyinfermionictopologicalorders |