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.

arXiv comment103 + 3 pages, many figures, many tables, comments welcome; v2 accepted for publication in Quantum; v3 added author contribution statement

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• Fusing Binary Interface Defects in Topological Phases: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ case
• On tensor network representations of the (3+1)d toric code
• Gauging the bulk: generalized gauging maps and holographic codes
• Gauging Defects in Quantum Spin Systems