Entanglement growth during thermalization in holographic systems

TL;DR

This paper analyzes the universal features of entanglement entropy growth during thermalization in holographic systems, revealing distinct regimes and potential bounds on entanglement growth rates.

Contribution

It provides a detailed holographic description of entanglement evolution during quenches, identifying regimes and geometric controls related to black hole horizons.

Findings

Identifies pre-local-equilibration quadratic growth regime.

Describes post-local-equilibration linear growth regime.

Suggests possible bounds on entanglement growth rates.

Abstract

We derive in detail several universal features in the time evolution of entanglement entropy and other nonlocal observables in quenched holographic systems. The quenches are such that a spatially uniform density of energy is injected at an instant in time, exciting a strongly coupled CFT which eventually equilibrates. Such quench processes are described on the gravity side by the gravitational collapse of a thin shell that results in a black hole. Various nonlocal observables have a unified description in terms of the area of extremal surfaces of different dimensions. In the large distance limit, the evolution of an extremal surface, and thus the corresponding boundary observable, is controlled by the geometry around and inside the event horizon of the black hole, allowing us to identify regimes of pre-local- equilibration quadratic growth, post-local-equilibration linear growth, a memory loss regime, and a saturation regime with behavior resembling those in phase transitions. We also discuss possible bounds on the maximal rate of entanglement growth in relativistic systems.