Unconventional Thermalization of a Localized Chain Interacting with an Ergodic Bath

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Abstract
The study of many-body localized (MBL) phases intrinsically links spectral properties with eigenstate characteristics: localized systems exhibit Poisson level statistics and area-law entanglement entropy, while ergodic systems display volume-law entanglement and follow random matrix theory predictions, including level repulsion. Here, we introduce the interacting Anderson Quantum Sun model, which significantly deviates from these conventional expectations. In addition to standard localized and ergodic phases, we identify a regime that exhibits volume-law entanglement coexisting with intermediate spectral statistics. We also identify another nonstandard regime marked by Poisson level statistics, sub-volume entanglement growth, and rare-event-dominated correlations, indicative of emerging ergodic instabilities. These results highlight unconventional routes of ergodicity breaking and offer fresh perspectives on how Anderson localization may be destabilized.

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