The paper classifies one-dimensional Abelian translationally covariant modulated symmetries via Jordan normal forms and derives their Goldstone actions, which modify the conventional theorem by type of symmetry.
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6 Pith papers cite this work. Polarity classification is still indexing.
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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.
Fragment classification is efficiently learnable by quantum neural networks under suitable conditions but resists known classical dequantization techniques.
The peak-valley mechanism organizes strong Hilbert space fragmentation in 1D spin chains by assigning emergent good quantum numbers to the heights and depths of peaks and valleys.
A disorder-free spin ladder model exhibits a reversed quantum disentangled liquid at strong rung coupling, where light spins thermalize and heavy spins localize, establishing a microscopic origin for quasi-MBL.
Any Hamiltonian can be recast via Fock basis change as a local 1D lattice theory whose dispersion relation and non-integrability depend on its spectrum.
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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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Peak-valley mechanism for Hilbert space fragmentation
The peak-valley mechanism organizes strong Hilbert space fragmentation in 1D spin chains by assigning emergent good quantum numbers to the heights and depths of peaks and valleys.