  The thermalization of isolated quantum many-body systems is deeply related to
fundamental questions of quantum information theory. While integrable or
many-body localized systems display non-ergodic behavior due to extensively
many conserved quantities, recent theoretical studies have identified a rich
variety of more exotic phenomena in between these two extreme limits. The
tilted one-dimensional Fermi-Hubbard model, which is readily accessible in
experiments with ultracold atoms, emerged as an intriguing playground to study
non-ergodic behavior in a clean disorder-free system. While non-ergodic
behavior was established theoretically in certain limiting cases, there is no
complete understanding of the complex thermalization properties of this model.
In this work, we experimentally study the relaxation of an initial
charge-density wave and find a remarkably long-lived initial-state memory over
a wide range of parameters. Our observations are well reproduced by numerical
simulations of a clean system. Using analytical calculations we further provide
a detailed microscopic understanding of this behavior, which can be attributed
to emergent kinetic constraints.
