For the root-of-unity XXZ chain, non-commuting transfer matrices generate an explicit Onsager algebra and duality defects obeying Z_N Tambara–Yamagami fusion rules.
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A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise conditions established via generalized gauging.
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
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Lattice non-invertible symmetry from non-commuting transfer matrices
For the root-of-unity XXZ chain, non-commuting transfer matrices generate an explicit Onsager algebra and duality defects obeying Z_N Tambara–Yamagami fusion rules.
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Lattice Models for Phases and Transitions with Non-Invertible Symmetries
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
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Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions
Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise conditions established via generalized gauging.
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.