Non-ergodic Quantum Dynamics in Highly Excited States of a Kinematically Constrained Rydberg Chain

Motivated by recent experimental advances in Rydberg atom quantum simulators, we study the possibility of quantum coherent many-body dynamics far from equilibrium. We identify a class of models which contain an extensive number of highly-excited energy eigenstates with low entanglement entropy, which are responsible for the persistent oscillations observed in recent experiments. We develop a novel non-perturbative forward-scattering method which quantitatively describes the structure of these eigenstates and predicts the frequency of the oscillations. Remarkably the existence of these states does not rely on Many Body Localisation and occurs despite almost all of the other eigenstates being thermal. Our study opens the way towards understanding the unusual case of quantum coherent states in otherwise thermalising many-body systems.