Out-of-time-ordered correlators in many-body localized systems

Understand

In many-body localized systems, propagation of information forms a light cone that grows logarithmically with time.

• However, local changes in energy or other conserved quantities typically spread only within a finite distance.
• Is it possible to detect the logarithmic light cone generated by a local perturbation from the response of a local operator at a later time? We numerically calculate various correlators in the random-field Heisenberg chain.
• While the equilibrium retarded correlator $A(t=0)B(t>0)$ is not sensitive to the unbounded information propagation, the out-of-time-ordered correlator $A(t=0)B(t>0)A(t=0)B(t>0)$ can detect the logarithmic light cone.