Symmetry-Enriched Topological Order in Tensor Networks

We have studied 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 was established. Tensor network representations of the topological defect superselection sectors were constructed for all domain walls. The emergent symmetry-enriched topological order was 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, were analyzed and the relationship between topological orders on either side of the transition were derived.