Stat-mech models with symmetries capture how proliferation of two non-Abelian anyons in D4 topological order parasitically condenses a shared Abelian anyon, destroying topological order while the trivial phase remembers which anyons condensed.
Hasse diagrams for gapless spt and ssb phases with non-invertible symmetries,
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Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
Any weakly integral fusion category admits a QCA-refined realization on tensor-product Hilbert spaces with QCA and symmetry indices fixed by the categorical data under defect assumptions.
PT symmetry enriches non-Hermitian critical points with topological nontriviality, robust edge modes, and a quantized imaginary subleading term in entanglement entropy scaling.
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).
E∞^{1,2}-type LSM anomalies lead to non-invertible symmetry breaking at type-II deconfined quantum critical points in 1D spin chains.
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.
citing papers explorer
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Statistical Mechanics and Symmetries of Non-Abelian Anyon Proliferation: From Deformation to Decoherence
Stat-mech models with symmetries capture how proliferation of two non-Abelian anyons in D4 topological order parasitically condenses a shared Abelian anyon, destroying topological order while the trivial phase remembers which anyons condensed.
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Twin Algebras: Condensable Algebras beyond Anyons
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
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Non-Invertible Symmetries on Tensor-Product Hilbert Spaces and Quantum Cellular Automata
Any weakly integral fusion category admits a QCA-refined realization on tensor-product Hilbert spaces with QCA and symmetry indices fixed by the categorical data under defect assumptions.
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PT symmetry-enriched non-unitary criticality
PT symmetry enriches non-Hermitian critical points with topological nontriviality, robust edge modes, and a quantized imaginary subleading term in entanglement entropy scaling.
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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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$E_\infty^{1,2}$-type Lieb-Schultz-Mattis anomalies, deconfined quantum critical points, and non-invertible symmetry breaking
E∞^{1,2}-type LSM anomalies lead to non-invertible symmetry breaking at type-II deconfined quantum critical points in 1D spin chains.
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Notes on (-2)-form symmetries
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
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Twin Phases: Intrinsic Deconfined Quantum Criticality
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.