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Quantum Networks
Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation
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Authors: Dominic J. Williamson, Nick Bultinck, Frank Verstraete
Year
2026
Paper ID
77330
Status
Peer-reviewed
Abstract Read
~2 min
Abstract Words
105
Citations
N/A
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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- This paper contributes to the Quantum Networks research area in the Quantum Articles archive.
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- 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.
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