Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation. (arXiv:1711.07982v1 [quant-ph])

We study symmetry-enriched topological order in two-dimensional tensor
network states by using graded matrix product operator algebras to represent
symmetry induced domain walls. A close connection to the theory of graded
unitary fusion categories is established. Tensor network representations of the
topological defect superselection sectors are constructed for all domain walls.
The emergent symmetry-enriched topological order is extracted from these
representations, including the symmetry action on the underlying anyons. Dual
phase transitions, induced by gauging a global symmetry, and condensation of a
bosonic subtheory, are analyzed and the relationship between topological orders
on either side of the transition is derived. Several examples are worked
through explicitly.

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