Charged Black Hole with String Cloud Deformation: Entanglement and Chaos

Abstract

We perform a holographic analysis of several quantum information theoretic observables entanglement entropy (EE), mutual information (MI), entanglement wedge cross section (EWCS), butterfly velocity ($v_B$) and thermo mutual information (TMI) in the background of charged AdS black hole deformed by a homogeneous string cloud. This configuration is dual to a large $\mathcal{N}_c$ strongly coupled field theory at finite temperature and finite chemical potential, in presence of quark cloud. We study how the entanglement structure and chaotic dynamics in the boundary theory are affected by the charge and backreaction. We find that both EE and EWCS increase monotonically with charge and backreaction, indicating enhanced correlations due to additional bulk degrees of freedom. On the other hand MI and TMI show a more intricate dependence backreaction tends to strengthen correlations, while increasing charge suppresses entanglement and makes the system more susceptible to scrambling. The analysis of the butterfly velocity indicates that both the presence of charge and the backreaction suppress the chaotic behavior of the system by reducing $v_B$. Furthermore, TMI exhibits a sharp transition under shockwave perturbations, with inter-boundary entanglement being entirely disrupted beyond a critical shock strength, which decreases with increasing charge.