Pole-skipping as order parameter to probe a quantum critical point

TL;DR

This paper introduces pole-skipping as a novel order parameter to identify a quantum critical point in a holographic system, linking quantum chaos, butterfly velocity, and phase transition detection.

Contribution

It demonstrates that pole-skipping points of the response function serve as new order parameters for quantum phase transitions in holographic models.

Findings

Butterfly velocity equals the speed of light at the critical point in one direction.

Pole-skipping based order parameters distinguish ordered and disordered phases.

Chiral magnetic effect is connected to quantum chaos phenomena.

Abstract

The holographic system described by Einstein-Maxwell-Chern-Simons dynamics in the bulk of AdS exhibits a chiral magnetic effect and a quantum critical point. Through numerical calculations, we find that the butterfly velocity can serve as a new identifier for the quantum critical point in this system. We show that the critical point is the point at which the butterfly velocity is equal to the speed of light in the direction of the magnetic field, while in the opposite direction the butterfly propagation vanishes. Furthermore, by studying the pole-skipping points of the response function of the operator dual to the tensor part of the metric perturbation in the bulk, we discover a set of order parameters that distinguish the two states of the system near the quantum critical point. Each of these order parameters is the sum of the absolute values of the real parts of momentum at all pole-skipping points associated with a particular frequency. This quantity vanishes in the disordered state while taking a positive value in the ordered state. In addition, our results confirm the idea that the chiral magnetic effect can manifest macroscopically through quantum chaos.