Charged Renyi entropies and holographic superconductors

Abstract

Charged Renyi entropies were recently introduced as a measure of entanglement between different charge sectors of a theory. We investigate the phase structure of charged Renyi entropies for CFTs with a light, charged scalar operator. The charged Renyi entropies are calculated holographically via areas of charged hyperbolic black holes. These black holes can become unstable to the formation of scalar hair at sufficiently low temperature; this is the holographic superconducting instability in hyperbolic space. This implies that the Renyi entropies can be non-analytic in the Renyi parameter n. We find the onset of this instability as a function of the charge and dimension of the scalar operator. We also comment on the relation between the phase structure of these entropies and the phase structure of a holographic superconductor in flat space.

21 pages, 6 figures

References in corpus (9)

• 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
• Thermodynamical Property of Entanglement Entropy for Excited States
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement Entropy in the O(N) model
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Charged Rényi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals

Cited by in corpus (11)

• Complexity Equals Anything II
• Symmetry decomposition of relative entropies in conformal field theory
• Supersymmetric Rényi Entropy in Five Dimensions
• Monodromy Defects from Hyperbolic Space
• Equipartition of Entanglement in Quantum Hall States
• Capacity of Entanglement in Local Operators
• A universal feature of charged entanglement entropy
• Symmetry Resolution in non-Lorentzian Field Theories
• Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
• Thermal Correction to Entanglement Spectrum for Conformal Field Theories
• Shape Deformations of Charged Rényi Entropies from Holography