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Abstract

In general, the dynamics of many-body quantum systems far-from-equilibrium is highly intricate, and it depends strongly on the initial conditions, the spatial geometry, and the type of the Hamiltonian. Nonetheless, at late times, almost all macroscopic systems will eventually lose memory of the initial state and thermalize. As a significant exception to this rule, strongly disordered systems can retain retrievable quantum correlations for long times, leading to a rich phenomenology ranging from anomalously slow relaxation to many-body localization (MBL).

This thesis studies the out-of-equilibrium dynamics of isolated, disordered quantum spin systems realized by a Rydberg quantum simulator where both the distribution of random coupling strengths and the type of the Hamiltonian can be tuned. In Part I, we observed sub-exponential, glassy dynamics well described by a stretched exponential law. This dynamics is independent of the type of Hamiltonian and the strength of disorder up to a critical value, showing a notion of universality in the relaxation dynamics of disordered systems far-from-equilibrium. A theoretical investigation revealed that the underlying nature leading to glassy dynamics is a scale-invariant distribution of interaction strengths. Part II reports on the discovery of the absence of thermalization in a quantum system out of thousands of spins. To achieve this, we developed a new protocol based on global magnetization measurements that can successfully distinguish thermalizing and non-thermalizing systems. Detailed exact numerical studies were able to confirm the breakdown of the Eigenstate Thermalization Hypothesis (ETH) for small strongly disordered systems of up to 16 spins. In addition, we have shown that pairs constitute effective integrals of motion providing thus an intuitive physical picture that also explains the universality of the relaxation dynamics. Both phenomena as described in Part I and II point toward the emergence of localization as the overarching principle governing out-of-equilibrium dynamics of disordered quantum spin systems.