Very General Holographic Superconductors and Entanglement Thermodynamics

TL;DR

This paper develops a comprehensive class of holographic superconductors with higher derivative couplings, analyzing their phase structure and entanglement entropy to understand their thermodynamic behavior in various black hole backgrounds.

Contribution

It introduces very general holographic superconductor models with multiple parameters and explores their phase diagrams and entanglement properties in R-charged black hole backgrounds.

Findings

Rich phase structures observed numerically and via free energy calculations.

Entanglement entropy accurately indicates phase transitions.

Differences in entanglement entropy between R-charged and Schwarzschild backgrounds.

Abstract

We construct and analyze holographic superconductors with generalized higher derivative couplings, in single R-charged black hole backgrounds in four and five dimensions. These systems, which we call very general holographic superconductors, have multiple tuning parameters and are shown to exhibit a rich phase structure. We establish the phase diagram numerically as well as by computing the free energy, and then validated the results by calculating the entanglement entropy for these systems. The entanglement entropy is shown to be a perfect indicator of the phase diagram. The differences in the nature of the entanglement entropy in R-charged backgrounds compared to the AdS-Schwarzschild cases are pointed out. We also compute the analogue of the entangling temperature for a subclass of these systems and compare the results with non-hairy backgrounds.