Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases
Name
Tang-2012-Interacting one-dimensional fermionic symmetry-protected topological phases.pdf
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244.69 KB
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Author(s)
Tang, Evelyn May Yin
Wen, Xiao-Gang
Date Issued
August 2012
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Tang, Evelyn, and Xiao-Gang Wen. “Interacting One-Dimensional Fermionic Symmetry-Protected Topological Phases.” Physical Review Letters 109.9 (2012). © 2012 American Physical Society
Version
Final published version
Abstract
In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, 0, Z[subscript 2], or Z. For example, noninteracting one-dimensional fermionic superconducting phases with S[subscript z] spin rotation and time-reversal symmetries are classified by Z. We show that with weak interactions, this classification reduces to Z[subscript 4]. Using group cohomology, one can additionally show that there are only four distinct phases for such one-dimensional superconductors even with strong interactions. Comparing their projective representations, we find that all these four symmetry-protected topological phases can be realized with free fermions. Further, we show that one-dimensional fermionic superconducting phases with Z[subscript n] discrete S[subscript z] spin rotation and time-reversal symmetries are classified by Z[subscript 4] when n is even and Z[subscript 2] when n is odd; again, all these strongly interacting topological phases can be realized by noninteracting fermions. Our approach can be applied to systems with other symmetries to see which one-dimensional topological phases can be realized with free fermions.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.109.096403
