Well-controlled synthetic quantum systems, such as ultracold atoms in optical lattices, offer intriguing possibilities to study complex many-body problems relevant to a variety of research areas, ranging from condensed matter to statistical physics. In particular, out-of-equilibrium phenomena constitute natural applications of quantum simulators, which have already successfully demonstrated simulations in regimes that are beyond reach using state-of-the-art numerical techniques.
This enables us to shed new light on fundamental questions about the thermalization of isolated quantum many-body systems. While generic models are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), violation of ETH is believed to occur mainly in two types of systems: integrable models and many-body localized systems. In between these two extreme limits there is, however, a whole range of models that exhibit more complex dynamics, for instance, due to an emergent fragmentation of the Hilbert space into exponentially many dynamically disconnected subspaces. A versatile platform that paves the way towards studying the rich variety of weak ergodic-breaking phenomena is the 1D Fermi-Hubbard model with a strong linear potential.
We have experimentally realized the tilted 1D Fermi-Hubbard model with ultracold K-atoms and have observed a robust memory of the initial state over a wide range of parameters, even down to small values of the tilt , which we explain microscopically via emergent kinetic constraints. Our measurements were performed in large fermionic systems of about 290 lattice sites for long evolution times up to 700 tunneling times. This regime is currently not accessible with state-of-the-art numerical techniques and we have used our experimental results to benchmark a novel more efficient numerical technique . In the large-tilt regime the non-ergodic behavior is explained by an emergent fragmentation of the many-body Hilbert space. We have realized this regime and confirmed experimentally that the effective description is accurate for the experimentally-accessible timescales . This paves the way for future studies on the initial-state dependent thermalization in the large tilt limit.
 S. Scherg, T. Kohlert, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, M. Aidelsburger, Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains, Nat. Comm. 12, 4490 (2021).
 B. Hebbe Madhusudhana, S. Scherg, T. Kohlert, I. Bloch, Monika Aidelsburger, Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator, arXiv:2105.06372 (2021); accepted in PRX Quantum.
 T. Kohlert, S. Scherg, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, M. Aidelsburger, Experimental realization of fragmented models in tilted Fermi-Hubbard chains, arXiv:2106.15586 (2021).