Chaos Near to the Critical Point: Butterfly Effect and Pole-Skipping

TL;DR

This paper investigates the behavior of chaos and pole-skipping near the critical point in holographic models, revealing how butterfly velocity signals criticality and how pole-skipping indicates complex correlation functions.

Contribution

It demonstrates that butterfly velocity can probe critical behavior and identifies pole-skipping as a sign of multivalued correlation functions in holographic models near criticality.

Findings

Butterfly velocity signals critical behavior near the phase transition.

Pole-skipping appears at chaos points, indicating multivalued correlation functions.

At all parameter points, $v_B^2 \,\geq\, c_s^2$, relating chaos and sound speed.

Abstract

We study the butterfly effect and pole-skipping phenomenon for the 1RCBH model which enjoys a critical point in its phase diagram. Using the holographic idea, we compute the butterfly velocity and interestingly find that this velocity can probe the critical behavior of this model. We calculate the dynamical exponent of this quantity near the critical point and find a perfect agreement with the value of the other quantity's dynamical exponent near this critical point. We also find that at chaos point, the phenomenon of pole-skipping appears which is a sign of a multivalued retarded correlation function. We briefly address the butterfly velocity and pole-skipping for the AdS-RN black hole solution which on its boundary a strongly coupled charged field theory lives. For both of these models, we find $v_B^2\geq c_s^2$ at each point of parameter space where $c_s$ is the speed of sound wave propagation.