# Information propagation in isolated quantum systems

## TL;DR

This paper investigates how information propagates in isolated quantum systems, revealing ballistic and sub-ballistic fronts depending on disorder strength, and linking entanglement growth with information dynamics.

## Contribution

It demonstrates the relationship between information front dynamics and entanglement entropy growth across different disorder regimes in quantum systems.

## Key findings

- Information propagates ballistically in weakly disordered systems.
- In strongly disordered systems, information front motion becomes sub-ballistic with a disorder-dependent exponent.
- The dynamical exponent for information front matches the entanglement entropy growth exponent.

## Abstract

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.