Gapped Domain Walls, Gapped Boundaries, and Topological Degeneracy
Name
PhysRevLett.114.076402.pdf
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325.26 KB
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Adobe PDF
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Author(s)
Lan, Tian
Wen, Xiao-Gang
Wang, Juven
Date Issued
February 2015
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Lan, Tian, Juven C. Wang, and Xiao-Gang Wen. “Gapped Domain Walls, Gapped Boundaries, and Topological Degeneracy.” Physical Review Letters 114.7 (2015). © 2015 American Physical Society
Version
Final published version
Abstract
Gapped domain walls, as topological line defects between (2+1)D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which (2+1)D topological orders must have gapless edge modes, namely, which (1+1)D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix W, whose entries are the fusion-space dimensions W[subscript ia], to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.114.076402
