Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
Bluvsteinet al., Controlling quantum many-body dy- namics in driven Rydberg atom arrays, Science371, 1355 (2021), arXiv:2012.12276 [quant-ph]
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An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.
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Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
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Hilbert Space Fragmentation and Gauge Symmetry
An emergent gauge symmetry valid only in a subset of sectors of the fragmented S=1 dipole-conserving spin chain enables exact quantum simulation of gauge theories using a non-gauge-invariant Hamiltonian.