Title: Observation of quantum thermalization restricted to Hilbert space fragments

Abstract: Quantum thermalization occurs in a broad class of systems from elementary particles to complex materials. Out-of-equilibrium quantum systems have long been understood to either thermalize or retain memory of their initial states, but not both. Here we achieve the first simultaneous demonstration of thermalization and memory in a quantum system. Using a Rydberg atom array, we observe quantum thermalization restricted to Hilbert space fragments, where the thermalized system retains characteristics of the initial configuration. Intriguingly, states from different subspaces do not thermalize with each other even when they have the same energy. Our work challenges established ideas of quantum thermalization while experimentally resolving the longstanding tension between thermalization and memory. These results may be applied to control entanglement dynamics in quantum processors and quantum sensors.