  We say that a quantum spin system is dynamically localized if the
time-evolution of local observables satisfies a zero-velocity Lieb-Robinson
bound. In terms of this definition we have the following main results: First,
for general systems with short range interactions, dynamical localization
implies exponential decay of ground state correlations, up to an explicit
correction. Second, the dynamical localization of random xy spin chains can be
reduced to dynamical localization of an effective one-particle Hamiltonian. In
particular, the isotropic xy chain in random exterior magnetic field is
dynamically localized.
