A remark on gapped domain walls between topological phases

Abstract

We give a mathematical definition of a gapped domain wall between topological phases and a gapped boundary of a topological phase. We then provide answers to some recent questions studied by Lan, Wang and Wen in condensed matter physics based on works of Davydov, Müger, Nikshych and Ostrik. In particular, we identify their tunneling matrix and a coupling matrix of Rehren, and show that their conjecture does not hold.

arXiv comment7 pages, minor fixes, references added

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Cited by in corpus (13)

• Boson Condensation in Topologically Ordered Quantum Liquids
• Higher central charges and topological boundaries in 2+1-dimensional TQFTs
• Boundary-bulk relation in topological orders
• Duality Defects in $E_8$
• A Remark on CFT Realization of Quantum Doubles of Subfactors. Case Index < 4
• Two-dimensional topological order and operator algebras
• Topological and nontopological degeneracies in generalized string-net models
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Soft symmetries of topological orders
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• A relative tensor product of subfactors over a modular tensor category
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders