Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation

Abstract: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.

Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); Quantum Algebra (math.QA)

arXiv:1711.07982 [quant-ph]

(or arXiv:1711.07982v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.1711.07982 Focus to learn more arXiv-issued DOI via DataCite

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