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arXiv · 1711.07982

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

Dominic J. Williamson·Nick Bultinck·Frank Verstraete
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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.

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Dominic J. Williamson, Nick Bultinck, Frank Verstraete. 2017-11-21. Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation. https://doi.org/10.22331/q-2026-09-01-2199

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