  Entanglement growth and out-of-time-order correlators (OTOC) are used to
assess the propagation of information in isolated quantum systems. In this
work, using large scale exact time-evolution we show that for weakly disordered
nonintegrable systems information propagates behind a ballistically moving
front, and the entanglement entropy growths linearly in time. For stronger
disorder the motion of the information front is algebraic and sub-ballistic and
is characterized by an exponent which depends on the strength of the disorder,
similarly to the sublinear growth of the entanglement entropy. We show that the
dynamical exponent associated with the information front coincides with the
exponent of the growth of the entanglement entropy for both weak and strong
disorder. We also demonstrate that the temporal dependence of the OTOC is
characterized by a fast\emph onnonexponential\emph default growth, followed by
a slow saturation after the passage of the information front. Finally,we
discuss the implications of this behavioral change on the growth of the
entanglement entropy.

Disordered Systems and Neural Networks;Quantum Gases;Strongly Correlated Electrons;High Energy Physics - Theory