Quantum· 2026Q1
Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation
- 12citations
- Q1SCImago
- 2026year
Short summary
Tensor network algebras are used to represent symmetry-induced domain walls, revealing a connection to graded unitary fusion categories and enabling the construction of topological defect superselection sectors.
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Key points
- Graded matrix product operator algebras represent symmetry-induced domain walls in 2D tensor network states.
- A connection is established between these algebras and graded unitary fusion categories.
- Tensor network representations of topological defect superselection sectors are constructed for all domain walls.
- The emergent symmetry-enriched topological order and symmetry action on anyons are extracted.
- Dual phase transitions and anyon condensation are analyzed, with relationships between topological orders derived.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Quantum, 2026 · DOI ↗
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Field: Atomic and Molecular Physics, and Optics
Atomic and Molecular Physics, and OpticsPhysics and Astronomy