Holographic thermalization in AdS-Gauss-Bonnet gravity for small entangled regions

TL;DR

This paper investigates how entanglement entropy evolves after a sudden quench in a holographic setting with Gauss-Bonnet gravity, focusing on small regions and comparing to large region behavior, revealing shape-dependent thermalization dynamics.

Contribution

It provides an analytical approximation for holographic entanglement entropy in Gauss-Bonnet gravity for small regions, highlighting differences from large region thermalization and phase transition characteristics.

Findings

Entanglement evolution exhibits a tsunami-like pattern.

Small regions show continuous phase transitions.

Large regions display shape-dependent breakdown of entanglement propagation.

Abstract

In this paper we study the propagation of entanglement entropy after a global instantaneous quench on the CFT boundary of AdS bulk. We consider the Gauss-Bonnet model as a higher curvature gravity model for which we correct the RT(HRT) proposal to compute the holographic entanglement entropy(HEE). To obtain an analytical solution we perform an approximation approach which bounds our computations to the small subregions and we compare its thermalization regimes to the result of large subsystem case. We can see tsunami picture where the evolution of entanglement breaks down for the large systems and so its details depends just on the shape and size of entangled region and also the used gravity model. We can see the phase transition in this regime is always continuous regardless the shape and size, in contrary with large subregions.