Well-controlled synthetic quantum systems, such as ultracold atoms in optical lattices, offer intriguing possibilities to study complex many-body problems in regimes that are beyond reach using state-of-the-art numerical techniques. This enables us, for instance, to shed new light on fundamental questions about the thermalization of isolated quantum many-body systems. Recently, a class of models has been identified that lies in between the extreme limits of thermal and localizing behavior. Here ergodicity-breaking occurs due to an emergent fragmentation of the many-body Hilbert space. A versatile platform that paves the way towards studying these phenomena is the 1D Fermi-Hubbard model with a strong linear potential.
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