Gapped Domain Walls, Gapped Boundaries, and Topological Degeneracy

• Main Authors: Lan, Tian (Author), Wen, Xiao-Gang (Contributor), Wang, Juven (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2015-02-19T19:08:48Z.
• Subjects: Article
• Online Access: Get fulltext

 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.