Introduces FTH as an extension of TH/SymTFT to type-I and type-II fracton orders, demonstrating boundary switches and dualities for X-cube and Haah's code via stabilizer formalism.
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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.
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
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).
BF Lagrangians for non-abelian DW theories (e.g. dihedral groups) are obtained by gauging H^(0) symmetries of abelian DW theories, with twisted cohomologies and condensation-defect operators verified by character-table linking.
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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Fracton Topological Holography
Introduces FTH as an extension of TH/SymTFT to type-I and type-II fracton orders, demonstrating boundary switches and dualities for X-cube and Haah's code via stabilizer formalism.
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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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Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
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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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On Lagrangians of Non-abelian Dijkgraaf-Witten Theories
BF Lagrangians for non-abelian DW theories (e.g. dihedral groups) are obtained by gauging H^(0) symmetries of abelian DW theories, with twisted cohomologies and condensation-defect operators verified by character-table linking.
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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.