Fermion decoration construction of symmetry-protected trivial order for fermion systems with any symmetry and in any dimension
Name
PhysRevB.100.235141.pdf
Size
1.22 MB
Format
Adobe PDF
Checksum (MD5)
abaac662c707abaf5b3a96c58e5967cb
Author(s)
Lan, Tian
Zhu, Chenchang
Wen, Xiao-Gang
Date Issued
2019
Journal
Physical Review B
Publisher
American Physical Society (APS)
Version
Final published version
Abstract
© 2019 American Physical Society. We use higher-dimensional bosonization and fermion decoration to construct exactly soluble interacting fermion models to realize fermionic symmetry-protected trivial (SPT) orders (which are also known as symmetry-protected topological orders) in any dimensions and for generic fermion symmetries Gf, which can be a nontrivial Z2f extension Z2Gb (where Z2f is the fermion-number-parity symmetry and Gb is the bosonic symmetry). This generalizes the previous results from group supercohomology of Gu and Wen (arXiv:1201.2648), where Gf is assumed to be Z2f×Gb. We find that the (d+1)-dimensional [(d+1)D] fermionic SPT phases with bosonic symmetry Gb and from fermion decoration construction can be described in a compact way using higher group homomorphism: BGb→φB(Z2,2;Z2,d). In fact, the fermion symmetry is more precisely described by the structure Z2f Gb SO∞ (or Z2f Gb O∞ with time-reversal symmetry). In this case the (d+1)D fermionic SPT phases are better described by B(Z2f Gb SO∞)→φB(SO∞,1;Z2,d) [or B(Z2f Gb O∞)→φB(O∞,1;Z2,d)].
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PHYSREVB.100.235141
