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arXiv:1708.07243 · Journal of High Energy Physics

Delocalizing entanglement of anisotropic black branes

Viktor Jahnke

Published Jan 1, 2018• 40 citations
arXivHTMLPDF

Abstract

We study the mutual information between pairs of regions on the two asymptotic boundaries of maximally extended anisotropic black branes. This quantity characterizes the local pattern of entanglement of the thermofield double states which are dual to these geometries. We analyze the disruption of the mutual information in anisotropic shock wave geometries and show that the entanglement velocity plays an important role in this phenomenon. Moreover, we compute several chaos-related properties of this system, such as the entanglement velocity, the butterfly velocity, and the scrambling time. We find that the butterfly velocity and the entanglement velocity violate the upper bounds proposed in [1-3], but remain bounded by their corresponding values in the infrared effective theory.

DOI
10.1007/jhep01(2018)102

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We study the mutual information between pairs of regions on the two asymptotic boundaries of maximally extended anisotropic black branes. This quantity characterizes the local pattern of entanglement of the thermofield double states which are dual to these geometries. We analyze the disruption of the mutual information in anisotropic shock wave geometries and show that the entanglement velocity plays an important role in this phenomenon. Moreover, we compute several chaos-related properties of this system, such as the entanglement velocity, the butterfly velocity, and the scrambling time. We find that the butterfly velocity and the entanglement velocity violate the upper bounds proposed in [1-3], but remain bounded by their corresponding values in the infrared effective theory.
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We compute the disruption of mutual information between the hemispherical subsystems on the left and right conformal field theories of a thermofield double state described by a Kerr geometry in AdS4{\mathrm{AdS}}_{4}AdS4​ due to shock waves along the equatorial plane. The shock waves and the subsystems considered respect the axisymmetry of the geometry. At late times, the disruption of the mutual information is given by the lengthening of the Hubeny-Rangamani-Takayanagi surface connecting the two subsystems; we compute the minimum value of the Lyapunov index-${\ensuremath{\lambda}}_{L}^{(\mathrm{min})}$ at late times and find that it is bounded by $\ensuremath{\kappa}=\frac{2\ensuremath{\pi}{T}_{H}}{(1\ensuremath{-}\ensuremath{\mu}\mathcal{L})}$, where $\ensuremath{\mu}$ is the horizon velocity, and L\mathcal{L}L is the angular momentum per unit energy of the shock wave. At very late times, we find the scrambling time for such a system is governed by $\ensuremath{\kappa}$ with $\ensuremath{\kappa}{t}_{*}=\mathrm{log}\mathcal{S}$ for large black holes with a large entropy S\mathcal{S}S. We also find a term that increases the scrambling time by $\mathrm{log}(1\ensuremath{-}\ensuremath{\mu}\mathcal{L}{)}^{\ensuremath{-}1}$ but which does not scale with the entropy of the Kerr geometry.
Using gauge/gravity duality, we explore a class of states of two CFTs with a large degree of entanglement, but with very weak local two-sided correlation. These states are constructed by perturbing the thermofield double state with thermal-scale operators that are local at different times. Acting on the dual black hole geometry, these perturbations create an intersecting network of shock waves, supporting a very long wormhole. Chaotic CFT dynamics and the associated fast scrambling time play an essential role in determining the qualitative features of the resulting geometries.
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’.
We compute the mutual information between finite intervals in two non-compact 2d CFTs in the thermofield double formulation after one of them has been locally perturbed by a primary operator at some time tω in the large c limit. We determine the time scale, called the scrambling time, at which the mutual information vanishes and the original entanglement between the thermofield double gets destroyed by the perturbation. We provide a holographic description in terms of a free falling particle in the eternal BTZ black hole that exactly matches our CFT calculations. Our results hold for any time tω . In particular, when the latter is large, they reproduce the bulk shock-wave propagation along the BTZ horizon description.
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.