Entanglement Entropy of Annulus in Holographic Thermalization

TL;DR

This paper studies how entanglement entropy in a holographic model evolves during thermalization, revealing phase transitions in the entanglement surface configurations depending on the annulus geometry and quench rate.

Contribution

It numerically analyzes the phase transitions of holographic entanglement entropy for an annular region during thermalization, highlighting the impact of geometry and quench speed.

Findings

Phase transitions depend on the ratio of annulus radii.

Double phase transitions occur during rapid quenches.

Slower quenches eliminate double phase transitions.

Abstract

The thermalization process of the holographic entanglement entropy (HEE) of an annular domain is investigated over the Vaidya-AdS geometry. We numerically determine the Hubeny-Rangamani-Takayanagi (HRT) surface which may be a hemi-torus or two disks, depending on the ratio of the inner radius to the outer radius of the annulus. More importantly, for some fixed ratio of two radii, it undergoes a phase transition or double phase transitions from a hemi-torus configuration to a two-disk configuration, or vice versa, during the thermalization. The occurrence of various phase transitions is determined by the ratio of two radii of the annulus. The rate of entanglement growth is also investigated during the thermal quench. The local maximal rate of entanglement growth occurs in the region with double phase transitions. Finally, if the quench process is fairly slow which may be controlled by the thickness of null shell, the region with double phase transitions vanishes.