Chiral symmetry on the edge of two-dimensional symmetry protected topological phases
Name
Chen-2012-Chiral symmetry on the edge.pdf
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290.54 KB
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Author(s)
Chen, Xie
Wen, Xiao-Gang
Date Issued
December 2012
Journal
Physical Review B
Publisher
American Physical Society
Citation
Chen, Xie, and Xiao-Gang Wen. “Chiral Symmetry on the Edge of Two-Dimensional Symmetry Protected Topological Phases.” Phys. Rev. B 86, no. 23 (December 2012). © 2012 American Physical Society
Version
Final published version
Abstract
Symmetry protected topological (SPT) states are short-range entangled states with symmetry. The boundary of a SPT phases has either gapless excitations or degenerate ground states, around a gapped bulk. Recently, we proposed a systematic construction of SPT phases in interacting bosonic systems, however it is not very clear what is the form of the low-energy excitations on the gapless edge. In this paper, we answer this question for two-dimensional (2D) bosonic SPT phases with Z[subscript N] and U(1) symmetry. We find that while the low-energy modes of the gapless edges are nonchiral, symmetry acts on them in a “chiral” way, i.e., acts on the right movers and the left movers differently. This special realization of symmetry protects the gaplessness of the otherwise unstable edge states by prohibiting a direct scattering between the left and right movers. Moreover, understanding of the low-energy effective theory leads to experimental predictions about the SPT phases. In particular, we find that all the 2D U(1) SPT phases have even integer quantized Hall conductance.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.86.235135
