Is the relaxation dynamics of spatially disordered quantum spin systems universal?

A major goal toward understanding far-from-equilibrium dynamics of quantum many-body systems consists in finding indications of universality in the sense that the dynamics no longer depends on microscopic details of the system. We realize a large range of many-body spin systems on a Rydberg atom quantum simulator by choosing appropriate Rydberg state combinations. We use this platform to compare the magnetization relaxation dynamics of disordered Heisenberg XX-, XXZ- and Ising Hamiltonians in a scalable fashion. After appropriate rescaling of evolution time, all the dynamics collapse onto a single curve, indicative of universal relaxation behavior. We find that this dynamics is approximately captured by an integrable model that only considers local pairs of spins. A detailed examination of the pair approximation not only facilitates a comprehensive discussion of the experimental data within the framework of prethermalization but also establishes in which sense the relaxation in disordered spin systems can be regarded as universal.