Slow propagation in some disordered quantum spin chains

Bruno Nachtergaele, Jake Reschke

Published 2019-06-24Version 1

We introduce the notion of transmission time to study the dynamics of disordered quantum spin chains and prove results relating its behavior to many-body localization properties. We also study two versions of the so-called Local Integrals of Motion (LIOM) representation of spin chain Hamiltonians and their relation to dynamical many-body localization. We prove that uniform-in-time dynamical localization expressed by a zero-velocity Lieb-Robinson bound implies the existence of a LIOM representation of the dynamics as well as a weak converse of this statement. We also prove that for a class of spin chains satisfying a form of exponential dynamical localization, sparse perturbations result in a dynamics in which transmission times diverge at least as a power law of distance, with a power for which we provide lower bound that diverges with increasing sparseness of the perturbation.