Exploring quantum correlations in a many-body localized system

An interacting quantum system that is subject to disorder may cease to thermalize due to localization of its constituents, thereby marking the breakdown of thermodynamics. We realize such a many-body-localized system in a disordered Bose-Hubbard chain and characterize its entanglement properties through particle fluctuations and correlations.

We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of non-local correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy - the hallmark of many-body localization. These results experimentally establish many-body localization as a qualitatively distinct phenomenon from localization in non-interacting, disordered systems.

Furthermore, we study the critical properties of the many-body localization transition. We identify a spatially separated, sparse-resonant structure of the system, which emerges at intermediate disorder strength and drives sub-diffusive particle motion. This structure persists into non-factorizable higher-order correlation functions. Our work identifies the many-body nature of the critical regime and lays a foundation for characterizing dynamic phases via high-order correlation.