On entanglement spreading from holography

TL;DR

This paper investigates entanglement entropy growth in holographic systems following a global quench, establishing bounds, analytical expressions, and relations to chaos, thereby advancing understanding of thermalization and information spreading in quantum field theories.

Contribution

It provides new holographic bounds on entanglement velocity and chaos-related speeds, analytical EE growth formulas, and bounds on EE growth rates for arbitrary shapes.

Findings

Proved holographic bounds on entanglement and butterfly effect velocities.

Derived analytical EE growth functions for large spherical regions.

Established bounds on EE growth rate for arbitrary shapes.

Abstract

A global quench is an interesting setting where we can study thermalization of subsystems in a pure state. We investigate entanglement entropy (EE) growth in global quenches in holographic field theories and relate some of its aspects to quantities characterizing chaos. More specifically we obtain four key results: 1. We prove holographic bounds on the entanglement velocity $v_E$ and the butterfly effect speed $v_B$ that arises in the study of chaos. 2. We obtain the EE as a function of time for large spherical entangling surfaces analytically. We show that the EE is insensitive to the details of the initial state or quench protocol. 3. In a thermofield double state we determine analytically the two-sided mutual information between two large concentric spheres separated in time. 4. We derive a bound on the rate of growth of EE for arbitrary shapes, and develop an expansion for EE at early times. In a companion paper arXiv:1608.05101, we put these results in the broader context of EE growth in chaotic systems: we relate EE growth to the chaotic spreading of operators, derive bounds on EE at a given time, and compare the holographic results to spin chain numerics and toy models. In this paper, we perform holographic calculations that provide the basis of arguments presented in that paper.