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arXiv:2507.10455 · Physical review. D/Physical review. D.

Charged black hole with string cloud deformation: Entanglement and chaos

Sanjay Pant, Shagun Kaushal, Arpit Maurya, Himanshu Parihar

Published Oct 7, 2025• 3 citations
arXivHTMLPDF

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 anti–de Sitter (AdS) black hole deformed by a homogeneous string cloud. This configuration is dual to a large 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. 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 v B 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.

DOI
10.1103/vxnt-zf5j

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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 anti–de Sitter (AdS) black hole deformed by a homogeneous string cloud. This configuration is dual to a large 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. 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 v B 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.
Abstract We perform a holographic study of the high and low temperature behaviours of logarithmic negativity (LN) and entanglement wedge cross section (EWCS) in a large N strongly coupled thermal field theory with critical point, having a well defined gravity dual known as 1RC black hole. The bulk theory accommodates a dimensionless parameter ξ\xi ξ ξ , proportional to the charge of the 1RC black hole. Holographically, ξ→2\xi \rightarrow 2ξ→2 ξ → 2 limit ensures an existence of a critical point in the dual boundary theory. We show that the logarithmic negativity in low and high temperature limits enhances with increasing ξ\xi ξ ξ . We analytically compute the EWCS in low and high temperature limits and find an agreement with the previously reported numerical results. We holographically explore the correlation between two identical copies of thermal field theory with critical point forming a thermofield double state (TFD) by computing the thermo mutual information (TMI). TMI shows an increasing behaviour with respect to the width of the boundary region. Furthermore, we study the chaotic behaviour of the field theory by analyzing a shock wave in the dual eternal 1 RC black hole and then estimate the degradation of TMI. The rate of such disruption of TMI slows down as the value of critical parameter ξ\xi ξ ξ takes higher values.
We investigate the holographic mixed-state entanglement measures in the Einstein-Maxwell-Scalar (EMS) theory. Several quantities are computed, including the holographic entanglement entropy (HEE), mutual information (MI), entanglement wedge cross-section (EWCS), and butterfly velocity (vBv_BvB​). Our findings demonstrate that these measures can effectively diagnose phase transitions. Notably, EWCS and MI, as mixed-state entanglement measures, exhibit behavior opposite to that of the HEE. Additionally, we study the butterfly velocity, a dynamic quantum information measure, and observe that it behaves differently from the static quantum information measures. We analyze the butterfly velocity and find that its non-monotonic behavior arises from the competition between two contributions in its expression, which the analytic structure suggests may be correlated with distinct physical interpretations. Moreover, we examine the scaling behavior of the holographic entanglement measures and find that all the critical exponents are equal to 111, which is twice that of the scalar field. We also explore the inequality between EWCS and MI, noting that the growth rate of MI consistently exceeds that of EWCS during phase transitions. These features are expected to be universal across thermodynamic phase transitions, with the inequalities becoming more significant as one moves away from the critical point.
We compute the entanglement entropy of Hawking radiation in a bath attached to a deformed eternal AdS black hole. This black hole is dual to the two identical strongly coupled large- N c thermal field theories, where each theory is backreacted (deformed) by the presence of a uniform static distribution of heavy fundamental quarks. In our observation we find that the entanglement entropy of Hawking radiation increases in a quadratic manner for an early time and linearly for the late time. The large time expression for the entanglement entropy of Hawking radiation is used to find the Page curve and Page time. After the Page time, the entanglement entropy saturates to a constant value due to the appearance of an island. We observe that introducing deformation (backreaction) delays the appearance of island and shifts the Page curve to a later time. Subsequently, the computation of the scrambling time reveals an increase with the backreaction parameter, suggesting a longer duration for information retrieval in the presence of deformation. Moreover, our analysis of the mutual information between the radiation subsystems shows that it vanishes at a critical time which increases with the deformation before the Page time. After the Page time, the appearance of island leads to the vanishing of mutual information between black hole subsystems and gives the time difference of the order of scrambling time.
Abstract We investigate the holographic mixed-state entanglement measures in the Einstein–Maxwell-Scalar (EMS) theory. Several quantities are computed, including the holographic entanglement entropy (HEE), mutual information (MI), entanglement wedge cross-section (EWCS), and butterfly velocity ( vBv_BvB​ v B ). Our findings demonstrate that these measures can effectively diagnose phase transitions. Notably, EWCS and MI, as mixed-state entanglement measures, exhibit behavior opposite to that of the HEE. Additionally, we study the butterfly velocity, a dynamic quantum information measure, and observe that it behaves differently from the static quantum information measures. We analyze the butterfly velocity and find that its non-monotonic behavior arises from the competition between two contributions in its expression, which the analytic structure suggests may be correlated with distinct physical interpretations. Moreover, we examine the scaling behavior of the holographic entanglement measures and find that all the critical exponents are equal to 1, which is twice that of the scalar field. We also explore the inequality between EWCS and MI, noting that the growth rate of MI consistently exceeds that of EWCS during phase transitions. These features are expected to be universal across thermodynamic phase transitions, with the inequalities becoming more significant as one moves away from the critical point.
We study entanglement in thermofield double states of strongly coupled conformal field theories by analyzing two-sided Reissner-Nordstr\"om solutions in anti--de Sitter space. The central object of study is the mutual information between a pair of regions, one on each asymptotic boundary of the black hole. For large regions the mutual information is positive and for small ones it vanishes; we compute the critical length scale, which goes to infinity for extremal black holes, of the transition. We also generalize the butterfly effect of Shenker and Stanford [J. High Energy Phys. 03 (2014) 067] to a wide class of charged black holes, showing that mutual information is disrupted upon perturbing the system and waiting for a time of order $\mathrm{log}E/\ensuremath{\delta}E$ in units of the temperature. We conjecture that the parametric form of this time scale is universal.
Abstract In the current manuscript we perform a systematic investigation about the effects of nonlocal interaction to the spread of quantum information in many body system. In particular, we have studied how nonlocality influence the existing bound on the growth rate of the commutator involving two local operators, the butterfly velocity. For this purpose, we consider the nonlocal theory on the worldvolume of N ≫ 1, NS5 branes arising in the limit of vanishing string coupling, the ‘little string theory’. A direct evidence of nonlocality can be realized from the ‘volume law’ behavior for the most dominant part of holographic entanglement entropy. We obtain the butterfly velocity by studying the dynamics of the near horizon geometry backreacted by a high energy quanta in the form of a shockwave resulting from an early perturbation on the corresponding thermofield double state. We observe that the butterfly velocity increases with the nonlocal scale of little string theory, the inverse Hagedorn temperature βh, indicating a faster rate of information spread due to the nonlocal interaction. The same conclusion follows as the disruption of two sided mutual information is observed to occur at a faster rate for higher values of βh. Finally, we realize a direct connection between the parameters of quantum chaos and the quasinormal modes for collective excitations through the phenomenon of ‘pole skipping’.