Phase transition of holographic entanglement entropy in massive gravity

TL;DR

This paper investigates the phase transitions of holographic entanglement entropy in massive gravity, revealing Van der Waals-like behavior and critical phenomena similar to thermal entropy, regardless of boundary volume.

Contribution

It demonstrates that the phase structure of holographic entanglement entropy mirrors thermal entropy's phase transitions in massive gravity, including first and second order transitions.

Findings

Existence of Van der Waals-like phase transitions in entanglement entropy.

Confirmation of equal area law at first order transition.

Determination of critical exponent for second order transition.

Abstract

The phase structure of holographic entanglement entropy is studied in massive gravity for the quantum systems with finite and infinite volumes, which in the bulk is dual to calculate the minimal surface area for a black hole and black brane respectively. In the entanglement entropy$-$temperature plane, we find for both the black hole and black brane there is a Van der Waals-like phase transition as the case in thermal entropy$-$temperature plane. That is, there is a first order phase transition for the small charge and a second order phase transition at the critical charge. For the first order phase transition, the equal area law is checked and for the second order phase transition, the critical exponent of the heat capacity is obtained. All the results show that the phase structure of holographic entanglement entropy is the same as that of thermal entropy regardless of the volume of the spacetime on the boundary.