Note on the butterfly effect in holographic superconductor models

TL;DR

This paper demonstrates that the butterfly effect, via butterfly velocity, can diagnose phase transitions in holographic superconductor models, showing discontinuities at critical points across different backgrounds.

Contribution

It introduces the use of butterfly velocity as a diagnostic tool for phase transitions in holographic superconductors, including charged black holes and anisotropic Q-lattice backgrounds.

Findings

Butterfly velocity's derivative with respect to temperature is discontinuous at critical points.

Butterfly velocity can signal thermal phase transitions in holographic models.

Discontinuities observed in both charged and anisotropic backgrounds.

Abstract

In this note we remark that the butterfly effect can be used to diagnose the phase transition of superconductivity in a holographic framework. Specifically, we compute the butterfly velocity in a charged black hole background as well as anisotropic backgrounds with Q-lattice structure. In both cases we find its derivative to the temperature is discontinuous at critical points. We also propose that the butterfly velocity can signalize the occurrence of thermal phase transition in general holographic models.