Note on Entanglement Temperature for Low Thermal Excited States in Higher Derivative Gravity

TL;DR

This paper explores the concept of entanglement temperature in low excited states within higher derivative gravity theories using holographic methods, revealing relationships with boundary CFT properties and extending to general excited states.

Contribution

It introduces a holographic approach to analyze entanglement temperature in higher derivative gravities and derives formulas applicable to general excited states.

Findings

Entanglement entropy relates to boundary CFT central charges.

Variance of entanglement entropy connects with subsystem energy.

The first law-like relation for entanglement is confirmed.

Abstract

We investigate the entanglement temperature of a small scale subsystem in low excited states by using holographic method. Especially, we study the entanglement entropy and entanglement temperature in higher derivative gravities which are considered as low thermal excitation of pure AdS gravity. We find that the entanglement entropy are related to the central charges of boundary CFT. The relation between the variance of entanglement entropy and energy of a small scale subsystem has been also obtained. Furthermore, the relation is consistent with the first law-like relation that is proposed by Phys. Rev. Lett. 110, 091602 (2013). Finally, we derive the formula of the variance of entanglement entropy in general excited states in gravity background with the Fefferman-Graham coordinates and the entanglement temperature can be figured out in special case.