String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
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5 Pith papers cite this work. Polarity classification is still indexing.
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Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
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.
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.
Review of integrable anyonic chains with new examples identified for su(2)_k, Tambara-Yamagami TY(Z_n), Fib x Fib, Fib x Ising, and preliminary results for Haagerup-Izumi categories.
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Constrained integrability and anyonic chains
Review of integrable anyonic chains with new examples identified for su(2)_k, Tambara-Yamagami TY(Z_n), Fib x Fib, Fib x Ising, and preliminary results for Haagerup-Izumi categories.