Comparative study of the butterfly velocity in holographic QCD models at finite temperature and chemical potential

Abstract: In this work, we study quantum chaos in a variety of holographic QCD models at finite temperature and chemical potentials. This includes the 1 R-Charge black hole (1RCBH) model, the 2 R-Charge black hole (2RCBH) model, a potential reconstruction-based analytic bottom-up model, and a numerical bottom-up model. All these models are different avatars of the Einstein-Maxwell-dilaton gravity action, distinguished by their specific choices of dilaton potentials and gauge-kinetic coupling functions. We focus on computing the chaos parameter, the butterfly velocity, using three distinct methods: entanglement wedge reconstruction, out-of-time-ordered correlators (OTOCs), and pole-skipping. We show that all three methods yield identical results for the butterfly velocity across all the holographic QCD models considered, further establishing the equivalence between the three approaches. Furthermore, we analyze in detail the behavior of the butterfly velocity as a function of chemical potential and temperature. Interestingly, a universal trend emerges across all models: the butterfly velocity increases/decreases with temperature/chemical potential for thermodynamically stable phases. Additionally, in the high-temperature limit, the butterfly velocity in all models approaches that of the chargeless plasma.