Communications in Mathematical Physics

, Volume 313, Issue 2, pp 351–373 | Cite as

Models for Gapped Boundaries and Domain Walls

  • Alexei Kitaev
  • Liang Kong


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.


Domain Wall Defect Line Simple Object Tensor Category Fusion Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.Institute for Advanced StudyTsinghua UniversityBeijingChina

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