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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Long, and Dominic V
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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.
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.
citing papers explorer
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Constructing Bulk Topological Orders via Layered Gauging
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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The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise
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.