Boundary degeneracy of topological order
Name
PhysRevB.91.125124.pdf
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513.78 KB
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Author(s)
Wen, Xiao-Gang
Wang, Juven
Date Issued
March 2015
Journal
Physical Review B
Publisher
American Physical Society
Citation
Wang, Juven C., and Xiao-Gang Wen. “Boundary Degeneracy of Topological Order.” Phys. Rev. B 91, no. 12 (March 2015). © 2015 American Physical Society
Version
Final published version
Abstract
We introduce the concept of boundary degeneracy, as the ground state degeneracy of topologically ordered states on a compact orientable spatial manifold with gapped boundaries. We emphasize that the boundary degeneracy provides richer information than the bulk degeneracy. Beyond the bulk-edge correspondence, we find the ground state degeneracy of the fully gapped edge modes depends on boundary gapping conditions. By associating different types of boundary gapping conditions as different ways of particle or quasiparticle condensations on the boundary, we develop an analytic theory of gapped boundaries. By Chern-Simons theory, this allows us to derive the ground state degeneracy formula in terms of boundary gapping conditions, which encodes more than the fusion algebra of fractionalized quasiparticles. We apply our theory to Kitaev's toric code and Levin-Wen string-net models. We predict that the Z[subscript 2] toric code and Z[subscript 2] double-semion model [more generally, the Z[subscript k] gauge theory and the U(1)[subscript k]×U(1)[subscript −k] nonchiral fractional quantum Hall state at even integer k] can be numerically and experimentally distinguished, by measuring their boundary degeneracy on an annulus or a cylinder.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.91.125124
