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

TL;DR

This paper demonstrates that out-of-time-ordered correlators can detect the logarithmic light cone in many-body localized systems, revealing information propagation not seen in traditional retarded correlators, and explores temperature effects on this phenomenon.

Contribution

It introduces a method to detect the logarithmic light cone in MBL systems using out-of-time-ordered correlators, linking them to Lieb-Robinson bounds and analyzing temperature dependence.

Findings

Out-of-time-ordered correlators reveal the logarithmic light cone.

Retarded correlators are insensitive to unbounded information spread.

Temperature influences the extent of the logarithmic light cone.

Abstract

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. We relate out-of-time-ordered correlators to the Lieb-Robinson bound in many-body localized systems, and show how to detect the logarithmic light cone with retarded correlators in specially designed states. Furthermore, we study the temperature dependence of the logarithmic light cone using out-of-time-ordered correlators.