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Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy

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arxiv 1408.6514 v2 pith:GZXR6T4F submitted 2014-08-27 cond-mat.str-el hep-thmath-phmath.CTmath.MP

classification cond-mat.str-elhep-thmath-phmath.CTmath.MP
keywords gappeddomaintopologicalwallsboundariesmanifoldscriteriadegeneracy
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abstract

Gapped domain walls, as topological line defects between 2+1D 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+1D topological orders must have gapless edge modes, namely which 1+1D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix $\mathcal W$, whose entries are the fusion-space dimensions $\mathcal W_{ia}$, 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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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