期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 351, 期 2, 页码 709-739出版社
SPRINGER
DOI: 10.1007/s00220-016-2748-y
关键词
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资金
- NSF [DMR-1506475]
- NSFC [11274192]
- John Templeton Foundation [39901]
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research
- Center of Mathematical Sciences and Applications at Harvard University
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1506475] Funding Source: National Science Foundation
A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category . In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry are classified, up to quantum Hall states, by the unitary modular tensor categories over and the modular extensions of each . In the case , we prove that the set of all modular extensions of has a natural structure of a finite abelian group. We also prove that the set of all modular extensions of , if not empty, is equipped with a natural -action that is free and transitive. Namely, the set is an -torsor. As special cases, we explain in detail how the group recovers the well-known group-cohomology classification of the 2+1D bosonic SPT orders and Kitaev's 16 fold ways. We also discuss briefly the behavior of the group under the symmetry-breaking processes and its relation to Witt groups.
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