Models for Gapped Boundaries and Domain Walls |
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Authors: | Alexei?Kitaev Email author" target="_blank">Liang?KongEmail author |
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Institution: | 1.California Institute of Technology,Pasadena,USA;2.Institute for Advanced Study,Tsinghua University,Beijing,China |
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Abstract: | We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category C{\mathcal C} as in the Levin-Wen model, whereas the boundary is associated with a module category over C{\mathcal C} . We also consider domain walls (or defect lines) between different bulk phases. A domain wall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions. |
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