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

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.