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Models for Gapped Boundaries and Domain Walls

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 \({\mathcal C}\) as in the Levin-Wen model, whereas the boundary is associated with a module category over \({\mathcal C}\) . 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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Correspondence to Liang Kong.

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Communicated by Y. Kawahigashi

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Kitaev, A., Kong, L. Models for Gapped Boundaries and Domain Walls. Commun. Math. Phys. 313, 351–373 (2012). https://doi.org/10.1007/s00220-012-1500-5

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  • DOI: https://doi.org/10.1007/s00220-012-1500-5

Keywords

  • Domain Wall
  • Defect Line
  • Simple Object
  • Tensor Category
  • Fusion Category