Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 53, Issue 23, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/ab7d60
Keywords
Levin-Wen models; fusion categories; topological phases of matter; topological quantum field theory
Categories
Funding
- Australian Research Council (ARC) [DP140100732, DP16010347]
- Perimeter Institute for Theoretical Physics
- Government of Canada through the Department of Innovation, Science and Economic Development Canada
- Province of Ontario through the Ministry of Economic Development, Job Creation and Trade
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We discuss domain walls and defects in topological phases occurring as the Drinfeld center of some fusion category. Domain walls between such phases correspond to bimodules between the fusion categories. Point defects correspond to functors between the bimodules. A domain wall structure consists of a planar graph with faces labeled by fusion categories. Edges are labeled by bimodules. When the vertices are labeled by point defects we get a compound defect. We present an algorithm, called the domain wall structure algorithm, for computing the compound defect. We apply this algorithm to show that the bimodule associator, related to the O-3 obstruction of Etingof et al (2010 Quantum Topol. 1 209), is trivial for all domain walls of Vec (Z/pZ). In the language of this paper, the ground states of the Levin-Wen model are compound defects. We use this to define a generalization of the Levin-Wen model with domain walls and point defects. The domain wall structure algorithm can be used to compute the ground states of these generalized Levin-Wen type models.
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