Scalable spin squeezing on random graphs requires spectral dimension control or sub-criticality, emerging from xy-ferromagnetic and percolation universality interplay.
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In fully connected models, integrability remains robust against non-extensive and extensive one-body perturbations but becomes extremely fragile under extensive two-body perturbations, which trigger chaos at infinitesimal strength within symmetry-defined energy bands and produce fragmented eigenstte
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Fragmented eigenstate thermalization versus robust integrability in long-range models
In fully connected models, integrability remains robust against non-extensive and extensive one-body perturbations but becomes extremely fragile under extensive two-body perturbations, which trigger chaos at infinitesimal strength within symmetry-defined energy bands and produce fragmented eigenstte