Experimental evidence for Hilbert-space fragmentation in tilted Fermi-Hubbard chains

Out-of-equilibrium phenomena constitute natural applications of quantum simulators based on ultracold atoms in optical lattices. We utilize them to explore fundamental questions about the thermalization of isolated quantum many-body systems. Generically, thermalization in such systems occurs according to the eigenstate thermalization hypothesis (ETH). In contrast, violation of ETH is believed to occur mainly in two types of systems: integrable models and many-body localized systems (MBL). In between these two extreme limits there is a whole range of models that exhibit more complex dynamics, for instance, due to an emergent fragmentation of the Hilbert space (HSF) into many dynamically disconnected subspaces. We have realized the tilted 1D Fermi-Hubbard model which lies at the interface of MBL and HSF and probe out-of-equilibrium dynamics in this model by preparing an initial charge-density wave state. We observe a robust memory of this initial state over a wide range of parameters. Furthermore, we find a strong initial-state dependent thermalization in the large tilt limit - a smoking-gun signature of Hilbert-space fragmentation.