Introduces pro-tensor networks as a categorified graphical framework for many-many-body theories, recovers the Levin-Wen model, characterizes particles as modules over promonads, and relaxes semisimplicity, finiteness, and rigidity assumptions.
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Topological holography for fermions,
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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.
Topological quantum critical points exhibit anomalous dynamical scaling in boundary dynamics and defect production due to edge modes, beyond conventional Kibble-Zurek scaling.
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).
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra, enabling braiding computations in the 3D SymTFT.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Derives exact bulk-boundary correspondence allowing extraction of edge-mode degeneracy from bulk entanglement spectrum in critical free-fermion systems of arbitrary dimensions.
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
citing papers explorer
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Pro-Tensor Network
Introduces pro-tensor networks as a categorified graphical framework for many-many-body theories, recovers the Levin-Wen model, characterizes particles as modules over promonads, and relaxes semisimplicity, finiteness, and rigidity assumptions.
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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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Anomalous Dynamical Scaling at Topological Quantum Criticality
Topological quantum critical points exhibit anomalous dynamical scaling in boundary dynamics and defect production due to edge modes, beyond conventional Kibble-Zurek scaling.
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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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Characterizing bulk properties of gapped phases by smeared boundary conformal field theories: Role of duality in unusual ordering
Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.
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Categorical Symmetries via Operator Algebras
The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra, enabling braiding computations in the 3D SymTFT.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
Derives exact bulk-boundary correspondence allowing extraction of edge-mode degeneracy from bulk entanglement spectrum in critical free-fermion systems of arbitrary dimensions.
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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.