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Understanding how closed quantum systems dynamically approach thermalequilibrium presents a major unresolved problem in statistical physics.Generically, it is expected that non-integrable quantum systems thermalize asthey comply with the Eigenstate Thermalization Hypothesis (ETH)}. A notableexception to this is the phenomenon of many-body localization, where theemergence of local conserved quantities prevents thermalization, which has beenobserved in finite low-dimensional systems. We study an ensemble of Heisenbergspins with a tunable distribution of random coupling strengths realized by aRydberg quantum simulator. The total magnetization as a function of externalfield after a quench serves as a probe for thermalization. We find that such anisolated quantum system exhibits a non-thermalizing regime despite beingnon-integrable. It is shown that thermalization can be restored by reducing thedisorder in the coupling strengths. As our system consists of up to 4000 spins,we thus show that closed quantum systems can fail to reach thermal equilibriumeven at system sizes approaching the thermodynamic limit.

Absence of thermalization in an interacting system of thousands of quantum spins