Note on entanglement temperature for low thermal excited states in higher derivative gravity

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 CFT living on the boundary. 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.

Aspects of holographic entanglement at finite temperature and chemical potential

“…Another interesting exercise would be to study entanglement entropy in charged black holes with higher derivative corrections, in which case the Ryu-Takayanagi prescription no longer applies [54] (see e.g. [55] as an example). Remarkably, a class of these theories admit charged black hole solutions with negative entropy [56]; it would be desirable to understand the implications for entanglement entropy.…”

Notes on quantum entanglement of local operators

“…Therefore, it is important to reveal the fundamental properties of (Rényi) entanglement entropy. Remarkable properties of (Rényi) entanglement entropy have been obvious over the past a few years [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. For example, a state is excited perturbatively so that the energy of its excitation is much smaller than the inverse of the subsystem size.…”

Holographic geometry of cMERA for quantum quenches and finite temperature

“…This will be related to the local quenches [42] and there have been examples of their gravity duals [43][44][45][46]. One more intriguing future problem is to explore universal properties of excited states from the viewpoint of cMERA (refer to recent results from holography and CFT calculations [47][48][49][50][51][52][53][54]). …”