Propagation of entanglement in one-dimensional models of many-body localization

An important and still unanswered fundamental question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of an initially unentangled state is studied for a 1D random-field XXZ Hamiltonian. Even for weak interactions, when the system is thought to be in a many-body localized phase, entanglement shows neither localized nor diffusive behavior: interactions act as a singular perturbation on the truly localized state with no interactions. The logarithmic time dependence of entanglement observed rather suggests a broad range of time scales typical of glassy behavior.