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Long-lived dark states, in which an experimentally accessible qubit is not inthermal equilibrium with a surrounding spin bath, are pervasive in solid-statesystems. We explain the ubiquity of dark states in a large class ofinhomogenous central spin models using the proximity to integrable lines withexact dark eigenstates. At numerically accessible sizes, dark states persist aseigenstates at large deviations from integrability, and the qubit retainsmemory of its initial polarization at long times. Although the eigenstates ofthe system are chaotic, exhibiting exponential sensitivity to smallperturbations, they do not satisfy the eigenstate thermalization hypothesis.Rather, we predict long relaxation times that increase exponentially withsystem size. We propose that this intermediate chaotic but non-ergodic regimecharacterizes mesoscopic quantum dot and diamond defect systems, as we see nonumerical tendency towards conventional thermalization with a finite relaxationtime.

Persistent dark states in anisotropic central spin models