A layered gauging method constructs (k+1)-dimensional topological orders, including fracton models like the X-cube, from k-dimensional symmetries such as subsystem, anomalous, or noninvertible ones.
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Anomalies of Global Symmetries on the Lattice
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Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
Develops local diagnostics for strong symmetries and strong-to-weak symmetry breaking via infinite-volume definitions and local charge coherence, introduces von Neumann symmetries, and derives an LSM-type anomaly constraint for quantum spin chains.
Parameterized families of toric code Hamiltonians realize em-duality pumping and higher-order anyon pumping, diagnosed by topological pumping into tensor-network bond spaces and corner modes.
Pauli stabilizer codes are classified via algebraic L-theory, yielding a bulk-boundary map to Clifford QCAs and a structural comparison with continuum framed TQFTs.
For finite 1-form symmetries in (2+1)D, onsiteability holds exactly when the 't Hooft anomaly meets an algebraic condition allowing 1-gauging; the symmetry can then be realized as transversal Pauli operators via ancillas and circuits.
Anomaly inflow on monodromy defects in anomalous symmetry theories defines them as domain walls inducing topological order, yielding protected chiral edge modes and adiabatic pumping of gapless degrees of freedom, verified in chiral symmetry examples on continuum and lattice.
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