Classification of symmetry-protected phases for interacting fermions in two dimensions
Name
PhysRevB.97.205109.pdf
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514.49 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Cheng, Meng
Bi, Zhen
You, Yi-Zhuang
Gu, Zheng-Cheng
Date Issued
May 2018
Journal
Physical Review B
Publisher
American Physical Society
Citation
Cheng, Meng et al. "Classification of symmetry-protected phases for interacting fermions in two dimensions." Physical Review B 97, 20 (May 2018): 205109 © 2018 American Physical Society
Version
Final published version
Abstract
Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H[superscript 3](G,U(1)). Later, group supercohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group supercohomology, and we also show that with an additional H[superscript 1](G,Z[subscript 2]) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G×Z[subscript 2][superscript f] is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.97.205109
