Quantum Many-Body Scarring in constrained models

Recent quench experiments in a quantum simulator of interacting Rydberg atoms demonstrated surprising long-lived, periodic revivals from certain low entanglement states, while apparently quick thermalization from others. Motivated by these findings, I will in this talk analyze the dynamics of a family of kinetically constrained spin models related to the experiments. By introducing a manifold of locally entangled spins, representable by a low-bond dimension matrix product state (MPS), I will derive "semiclassical" equations of motion for them. I find that they host isolated, unstable periodic orbits, the presence of which captures the long-lived oscillations and gives rise to slow relaxation of local observables from certain initial configurations. This thus represents a form of weak breaking of ergodicity in dynamics. Our results are reminiscent of the phenomenon of quantum scarring in single-particle chaotic systems which is rooted in classical unstable periodic orbits, and complement the explanation of the recurrences given by [Nature Physics (2018), doi:10.1038/s41567-018-0137-5], in terms of motion over special nonergodic many-body eigenstates, suggestively dubbed `quantum many-body scars'.