  An important step towards a comprehensive understanding of
far-from-equilibrium dynamics of quantum many-body systems is the
identification of unifying features that are independent of microscopic details
of the system. We experimentally observe such robust features in the
magnetization relaxation dynamics of disordered Heisenberg XX-, XXZ- and Ising
Hamiltonians. We realize these Heisenberg spin models with tunable anisotropy
parameter and power-law interactions in an ensemble of Rydberg atoms by
encoding the spin in suitable Rydberg state combinations. We consistently
observe stretched-exponential relaxation of magnetization for all considered
spin models, collapsing onto a single curve after appropriate rescaling of
time. This robust short-time relaxation behavior is explained by a perturbative
treatment that exploits the strong disorder in pairwise couplings, which leads
to a description in terms of approximately independent pairs of spins. In
numerical simulations of small systems, we show that these pairs of spins
constitute approximate local integrals of motion, which remain at least
partially conserved on a timescale exceeding the duration of the relaxation
dynamics of the magnetization.
