Holographic Phases of Renyi Entropies

Abstract

We consider Renyi entropies of conformal field theories in flat space, with the entangling surface being a sphere. The AdS/CFT correspondence relates this Renyi entropy to that of a black hole with hyperbolic horizon; as the Renyi parameter $n$ increases the temperature of the black hole decreases. If the CFT possesses a sufficiently low dimension scalar operator the black hole will be unstable to the development of hair. Thus, as $n$ is varied, the Renyi entropies will exhibit a phase transition at a critical value of $n$. The location of the phase transition, along with the spectrum of the reduced density matrix $\rho$, depends on the dimension of the lowest dimension non-trivial scalar operator in the theory.

21 pages, 7 figures, v3 - References added. Neumann boundary conditions added in section 5

References in corpus (11)

• Building an AdS/CFT superconductor
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Towards a derivation of holographic entanglement entropy
• Entanglement spectrum in one-dimensional systems
• Colorful horizons with charge in anti-de Sitter space
• Entanglement Entropy in the O(N) model
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Holographic Rényi Entropies at Finite Coupling
• Renyi extrapolation of Shannon entropy
• A New Instability of the Topological black hole

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