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.
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Acknowledgments
We would like to thank Ali Davody, Matthias Kaminski and Dima Kharzeev for fruitful discussions. N.A. thanks the Instituto de Física Teórica, IFT-UAM/CSIC and the Institute for Theoretical Physics of Goethe University for their hospitality when this work was completed. N.A. was funded by Lanzhou University’s “Double First-Class” start-up fund 561119208. The research of K.L. is supported through the grants CEX2020-001007-S and PID2021-123017NB-100, PID2021-127726NB-I00 funded by MCIN/AEI/10.13039/501100011033 and by ERDF “A way of making Europe”.
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Abbasi, N., Landsteiner, K. Pole-skipping as order parameter to probe a quantum critical point. J. High Energ. Phys. 2023, 169 (2023). https://doi.org/10.1007/JHEP09(2023)169
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DOI: https://doi.org/10.1007/JHEP09(2023)169