Conductivity and entanglement entropy of high dimensional holographic superconductors

Abstract

We investigate the dependence of the conductivity and the entanglement entropy on the space-time dimensionality $d$ in two holographic superconductors: one dual to a quantum critical point with spontaneous symmetry breaking, and the other modeled by a charged scalar that condenses at a sufficiently low temperature in the presence of a Maxwell field. In both cases the gravity background is asymptotically Anti de Sitter (AdS). In the large $d$ limit we obtain explicit analytical results for the conductivity at zero temperature and the entanglement entropy by a $1/d$ expansion. We show that the entanglement entropy is always smaller in the broken phase. As dimensionality increases, the entanglement entropy decreases, the coherence peak in the conductivity becomes narrower and the ratio between the energy gap and the critical temperature decreases. These results suggest that the condensate interactions become weaker in high spatial dimensions.

38 pages, 7 figures

References in corpus (13)

• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Lectures on Holographic Superfluidity and Superconductivity
• Effective Holographic Theories for low-temperature condensed matter systems
• Holographic Superconductors with Various Condensates
• An Analytic Holographic Superconductor
• The gravity dual to a quantum critical point with spontaneous symmetry breaking
• Holographic Entanglement Entropy in Insulator/Superconductor Transition
• Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion
• Dimensional dependence of the metal-insulator transition
• Analytical study on holographic superconductors with backreactions
• Holographic entanglement entropy in general holographic superconductor models
• A general holographic metal/superconductor phase transition model
• Low temperature properties of holographic condensates

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