Holographic Renyi entropies from hyperbolic black holes with scalar hair

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.

30 pages, 5 figures; v2: improved, published version; v3: typos corrected

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Cited by in corpus (5)

• Holographic complexity of hyperbolic black holes
• Negative R$\acute{\text{e}}$nyi entropy and Brane intersection
• Holographic supersymmetric Renyi entropies from hyperbolic black holes with scalar hair
• Spectral Projections for Density Matrices in Quantum Field Theories
• Extended Holographic Rényi Entropy and hyperbolic black hole with scalar hair