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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Log-depth nonlocal unitary circuits realize exact Z2 and Zn KW dualities that map arbitrary SRE states to LRE duals in the symmetric sector.
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.
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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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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Shallow Unitary Circuits for Kramers-Wannier Dualities
Log-depth nonlocal unitary circuits realize exact Z2 and Zn KW dualities that map arbitrary SRE states to LRE duals in the symmetric sector.
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From gauging to duality in one-dimensional quantum lattice models
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.
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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.