A ribbon ZX calculus is defined for 2D Yang-Mills theory via the Hopf Frobenius structure of the group algebra, which matches 2D TQFT diagrammatics.
Generalized Kramers– Wannier self-duality in Hopf–Ising models
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Non-invertible Gauss laws on lattices preserve Haag duality exactly only on cuspless regions; cusped regions require a collar, and group double models satisfy disjoint additivity.
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.
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.
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
citing papers explorer
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A ribbon ZX calculus for gauge theory
A ribbon ZX calculus is defined for 2D Yang-Mills theory via the Hopf Frobenius structure of the group algebra, which matches 2D TQFT diagrammatics.
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Algebraic locality and non-invertible Gauss laws
Non-invertible Gauss laws on lattices preserve Haag duality exactly only on cuspless regions; cusped regions require a collar, and group double models satisfy disjoint additivity.
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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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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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Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
- Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions