Kinetically constrained dynamics and electron-phonon interactions in Rydberg quantum simulators

Rydberg quantum simulators, i.e. highly excited atoms held in optical tweezer arrays, are amongst the most advanced platforms for the implementation and study of strongly interacting spin systems. An interesting dynamical regime is reached when one atom that is brought to a Rydberg states facilitates the excitation of another nearby one. The resulting dynamics can be similar to that of epidemic spreading and also may form an ingredient for observing non-equilibrium phase transitions. In my talk I will discuss recent results concerning the analysis of constrained Rydberg spin dynamics in the presence of disorder which is caused by the coupling of electronic degrees of freedom and lattice vibrations. I will focus on incoherent and coherent regimes, discussing the breaking of ergodicity and the dressing of facilitated spins by phonons, respectively.