Symmetry protected topological orders and the group cohomology of their symmetry group
Massachusetts Institute of Technology · University of California, Berkeley · +3 more institutions
Abstract
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase of spin-1 chain is the first example of SPT phases which is protected by SO(3) spin rotation symmetry. The topological insulator is another example of SPT phases which are protected by U (1) and timereversal symmetries. In this paper, we show that interacting bosonic SPT phases can be systematically described by group cohomology theory: Distinct d-dimensional bosonic SPT phases with on-site symmetry G (which may contain antiunitary time-reversal symmetry) can be labeled by the elements in H…
Citation impact
- FWCI
- 63.86
- Percentile
- 100%
- References
- 93
Authors
4- XCXie ChenCorresponding
Massachusetts Institute of Technology, University of California, Berkeley
- ZGZheng‐Cheng Gu
California Institute of Technology
- ZLZheng-Xin Liu
Massachusetts Institute of Technology, Tsinghua University
- XWXiao-Gang Wen
Perimeter Institute, Massachusetts Institute of Technology, Tsinghua University
Topics & keywords
- Physics
- Topological insulator
- Degenerate energy levels
- Homogeneous space
- Sigma model
- Global symmetry
- Symmetry protected topological order
- Symmetry group
Funding
- NSNational Science FoundationAwards: NSFC 11274192, 1005541, NSFC 11074140, DMR-1005541, PHY05-51164
- GOGovernment of Canada
- NNNational Natural Science Foundation of ChinaAwards: 11274192, NSFC 11274192, NSFC 11074140, 11074140
- ICIndustry Canada
- IPInstitut Périmètre de physique théorique
- DODivision of Materials Research