Charged black hole with string cloud deformation: Entanglement and chaos

We perform a holographic analysis of several quantum information-theoretic observables—entanglement entropy (EE), mutual information (MI), entanglement wedge cross section (EWCS), butterfly velocity ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>v</a:mi> <a:mi>B</a:mi> </a:msub> </a:math> ), and thermo mutual information (TMI)—in the background of charged anti–de Sitter (AdS) black hole deformed by a homogeneous string cloud. This configuration is dual to a large <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi mathvariant="script">N</c:mi> <c:mi>c</c:mi> </c:msub> </c:math> 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. In our observation we find that both EE and EWCS increase monotonically with charge and backreaction, indicating enhanced correlations due to additional 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 <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>v</f:mi> <f:mi>B</f:mi> </f:msub> </f:math> indicates that the presence of charge and the backreaction suppress the chaotic behavior of the system by. Furthermore, TMI exhibits a sharp transition under shockwave perturbations, with interboundary entanglement being entirely disrupted beyond a critical shock strength, which decreases with increasing charge.