A concrete lattice model realizing a type-IV mixed anomaly yields emergent higher-categorical symmetries upon gauging, and the same framework applied to Lieb-Schultz-Mattis systems produces modulated symmetries whose realization is intrinsically defect-dependent.
Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
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Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.