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The holographic system described by Einstein-Maxwell-Chern-Simons dynamics inthe bulk of AdS exhibits a chiral magnetic effect and a quantum critical point.Through numerical calculations, we find that the butterfly velocity can serveas a new identifier for the quantum critical point in this system. We show thatthe critical point is the point at which the butterfly velocity is equal to thespeed of light in the direction of the magnetic field, while in the oppositedirection the butterfly propagation vanishes. Furthermore, by studying thepole-skipping points of the response function of the operator dual to thetensor part of the metric perturbation in the bulk, we discover a set of orderparameters that distinguish the two states of the system near the quantumcritical point. Each of these order parameters is the sum of the absolutevalues of the real parts of momentum at all pole-skipping points associatedwith a particular frequency. This quantity vanishes in the disordered statewhile taking a positive value in the ordered state. In addition, our resultsconfirm the idea that the chiral magnetic effect can manifest macroscopicallythrough quantum chaos.

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