Holographic Renyi entropies from hyperbolic black holes with scalar hair

TL;DR

This paper analytically computes Renyi entropies using hyperbolic black holes with scalar hair, revealing phase transition effects and expressing the entanglement spectrum through Bell polynomials, with results confirmed numerically.

Contribution

It introduces a new analytical method to calculate Renyi entropies from hyperbolic black holes with scalar hair, extending previous models and analyzing phase transition impacts.

Findings

Discontinuities in Renyi entropies at phase transitions

Expression of entanglement spectrum via Bell polynomials

Agreement between analytical and numerical results

Abstract

The Renyi entropies as a generalization of the entanglement entropy imply much more information. We analytically calculate the Renyi entropies (with a spherical entangling surface) by means of a class of neutral hyperbolic black holes with scalar hair as a one-parameter generalization of the MTZ black hole. The zeroth-order and third-order phase transitions of black holes lead to discontinuity of the Renyi entropies and their second derivatives, respectively. From the Renyi entropies that are analytic at $n=\infty$, we can express the entanglement spectrum as an infinite sum in terms of the Bell polynomials. We show that the analytic treatment is in agreement with numerical calculations for the low-lying entanglement spectrum in a wide range of parameters.