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Peer-reviewedCC BYQuantum

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

  • Dominic J. Williamson1
  • Nick Bultinck2
  • Frank Verstraete2
  1. 1Vienna Center for Quantum Technology, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
  2. 2Department of Physics and Astronomy, Ghent University, Krijgslaan 281 S9, B-9000 Ghent, Belgium
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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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Cite

BibTeXRIS
BibTeX
@article{williamson2026symmetryenriched,
  title = {{Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation}},
  author = {Dominic J. Williamson and Nick Bultinck and Frank Verstraete},
  journal = {Quantum},
  year = {2026},
  month = sep,
  doi = {10.22331/q-2026-09-01-2199},
  url = {https://doi.org/10.22331/q-2026-09-01-2199},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation
AU  - Dominic J. Williamson
AU  - Nick Bultinck
AU  - Frank Verstraete
PY  - 2026
DA  - 2026/09/01
JO  - Quantum
DO  - 10.22331/q-2026-09-01-2199
UR  - https://doi.org/10.22331/q-2026-09-01-2199
AB  - 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.
SN  - 2521-327X
ER  -