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Quantum spin systems with kinetic constraints have become paradigmatic forexploring collective dynamical behaviour in many-body systems. Here we discussa facilitated spin system which is inspired by recent progress in therealization of Rydberg quantum simulators. This platform allows to control andinvestigate the interplay between facilitation dynamics and the coupling ofspin degrees of freedom to lattice vibrations. Developing a minimal model, weshow that this leads to the formation of polaronic quasiparticle excitationswhich are formed by many-body spin states dressed by phonons. We investigate indetail the properties of these quasiparticles, such as their dispersionrelation, effective mass and the quasiparticle weight. Rydberg lattice quantumsimulators are particularly suited for studying this phonon-dressed kineticallyconstrained dynamics as their exaggerated length scales permit thesite-resolved monitoring of spin and phonon degrees of freedom.

Vibrational dressing in Kinetically Constrained Rydberg Spin Systems