The chiral anomaly is extended to mixed states via symmetry-charge flow derived algebraically from symmetry and flux-insertion operators, restoring universality for Abelian symmetries in fermionic and bosonic systems.
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A Rokhsar-Kivelson-type construction turns classical or non-fragmented models into quantum fragmented Hamiltonians whose Krylov sectors require an entangled basis to resolve.
Measurement-only circuits realize gapless SPT phases with nontrivial edge states at criticality, including symmetry-enriched percolation in Ising models and persistent Z4 gSPT phases mapped to Majorana loop models.
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Quantum Fragmentation
A Rokhsar-Kivelson-type construction turns classical or non-fragmented models into quantum fragmented Hamiltonians whose Krylov sectors require an entangled basis to resolve.