Abstract

Out-of-time-order correlators (OTOC) are used
to study the propagation of local information in isolated quantum systems.
I will discuss recent results using large scale exact time-evolution
for up to L=31 spins 1/2 and show that for
weakly disordered nonintegrable systems information propagates behind
a ballistically moving front, while the entanglement entropy growths
linearly in time. For stronger disorder the motion of the information
front is algebraic and sub-ballistic with a disorder strength
dependent exponent which depends on the strength of the disorder,
similarly to
the sublinear growth of the entanglement entropy. 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 and the temporal
dependence of the OTOC is characterized by a fast nonexponential
growth, followed by a slow saturation after the passage of the
information front. Finally, I will mention the implications of this
behavioral change on the growth of the entanglement entropy.