Abstract
The holographic superconductors, as one of the most important application of gauge/gravity duality, promote the study of strongly coupled superconductors via classical general relativity living in one higher dimension. One of the interesting properties in holographic superconductor is the appearance of first and second order phase transitions. Recently, another active studies in holographic framework is the holographic entanglement entropy and complexity evaluated from gravity side. In this note, we study the properties of the holographic entanglement entropy and complexity crossing both first and second order phase transitions in Stückelberg superconductor. We find that they behave differently in two types of phase transitions. We argue that holographic entanglement entropy and complexity conjectured with the volume can also be a possible probe to the type of superconducting phase transition.
Highlights
The holographic superconductors, as one of the most important application of gauge/gravity duality, promote the study of strongly coupled superconductors via classical general relativity living in one higher dimension
We study the properties of the holographic entanglement entropy and complexity crossing both first and second order phase transitions in Stuckelberg superconductor
We firstly reviewed the holographic superconductor phase transition in the Stuckelberg model with F (ψ) = ψ2 + c4ψ4
Summary
The AdS/CFT correspondence [1–3], has made significant progress and development. The first proposal on holographic s-wave superconductor in probe limit was found to undergo a second order phase transition from normal state[5]. Later, It was addressed in [12] that the holographic superconductor via the Stuckelberg mechanism allows the first order phase transition to occur when the model parameter surpasses a critical value, which was extended in [13–15]. Similar to the holographic entanglement entropy, at the second order phase transition temperature, the complexity is continuous and its slope in terms of the temperature have a jump, while in the first order phase transition case, the complexity presents a jump at the critical temperature.
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