Models for gapped boundaries and domain walls

Details Models for gapped boundaries and domain walls Models for gapped boundaries and domain walls

2011-04-26

arxiv.org/abs/1104.5047v2

Physics

Condensed Matter

Strongly Correlated Electrons

20 pages, references are added

Scientific paper

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 $\calC$ as in the Levin-Wen model, whereas the boundary is associated with a module category over $\calC$. 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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