Entanglement Entropy and Thermal Phase Transitions from Curvature Singularities

TL;DR

This paper explores how bulk curvature singularities in holographic models influence entanglement entropy and phase transitions, revealing that singularities can lead to either first or second order transitions depending on their nature.

Contribution

It provides a unified analysis of entanglement entropy and thermodynamics in a class of solvable dilaton-gravity backgrounds, linking phase transition order to the type of bulk singularity.

Findings

Singular backgrounds are confining if the singularity is at the boundary or is a linear dilaton.

First order phase transitions occur when the singularity cuts off spacetime.

Second order phase transitions are associated with linear dilaton singularities.

Abstract

We study holographic entanglement entropy and revisit thermodynamics and confinement in the dilaton-gravity system. Our analysis focuses on a solvable class of backgrounds that includes AdS and linear dilaton spacetimes as particular cases, with some results extended to general warped metrics. A general lesson is that the behavior of the holographic theory is tied to the bulk curvature singularities. We find that a singular background is confining if and only if i) the singularity coincides with a boundary or ii) it is the linear dilaton. In the former case, for which the singularity cuts off spacetime, we demonstrate that both entanglement entropy and thermodynamics exhibit a first order phase transition. In the linear dilaton case we find instead that both entanglement entropy and thermal phase transitions are of second order. Additionally, along the process we thoroughly derive the radion effective action at quadratic order.