Holographic information theoretic quantities for Lifshitz black hole

Karar, Sourav; Gangopadhyay, Sunandan

doi:10.1140/epjc/s10052-020-8091-7

Cited by 5 publications

(4 citation statements)

References 58 publications

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“…In the limit z = 1 and θ = 0, the above equation reads G F,mm ∝ l d+2 which agrees with the result obtained in [47]. The Fisher information corresponding to the Lifshitz type solutions can be found in [48].…”

Section: Relative Entropy and The Fisher Information Metricsupporting

confidence: 87%

Holographic study of entanglement and complexity for mixed states

Saha,

Gangopadhyay

2021

Preprint

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In this paper, we holographically quantify the entanglement and complexity for mixed states by following the prescription of purification. The bulk theory we consider in this work is a hyperscaling violating solution, characterized by two parameters, hyperscaling violating exponent θ and dynamical exponent z. This geometry is dual to a non-relativistic strongly coupled theory with hidden Fermi surfaces. For entanglement, we compute the holographic analogy of entanglement of purification (EoP), denoted as the minimal area of the entanglement wedge cross section and observe the effects of z and θ. On the other hand, in order to probe the mixed state complexity we compute the mutual complexity (∆C) for the BTZ black hole and the hyperscaling violating geometry by incorporating the holographic subregion complexity conjecture. Furthermore, various aspects of holographic entanglement entropy such as entanglement Smarr relation and Fisher information metric has also been studied.

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Section: Relative Entropy and The Fisher Information Metricsupporting

confidence: 87%

Holographic study of entanglement and complexity for mixed states

Saha,

Gangopadhyay

2021

Preprint

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“…Upto d = d c , connected phase is the physical whereas beyond d > d c disconnected phase is physical. Some recent works in this direction can be found in [35,52,[63][64][65][66][67][68][69][70][71][72][73]. We have depicted this fact in Fig.…”

Section: Computation Of Holographic Entanglement Entropymentioning

confidence: 79%

“…It is to be noted that in the above expression we have kept terms upto O T 4 . The change in the HEE due to thermal excitation plays a crucial role in context of entanglement thermodynamics [58][59][60][61][62]. In the right panel of figure 7, we have graphically represented a 2 SEE | finite l a as a function of (l/a) (given in eq.…”

Section: Jhep02(2022)192mentioning

confidence: 99%

Entanglement wedge cross-section for noncommutative Yang-Mills theory

Chowdhury

Saha

Gangopadhyay

2022

J. High Energ. Phys.

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The signature of noncommutativity on various measures of entanglement has been observed by considering the holographic dual of noncommutative super Yang-Mills theory. We have followed a systematic analytical approach in order to compute the holographic entanglement entropy corresponding to a strip like subsystem of length l. The relationship between the subsystem size (in dimensionless form) $$ \frac{l}{a} $$ l a and the turning point (in dimensionless form) introduces a critical length scale $$ \frac{l_c}{a} $$ l c a which leads to three domains in the theory, namely, the deep UV domain (l < lc; aut » 1, aut ∼ aub), deep noncommutative domain (l > lc, aub> aut » 1) and deep IR domain (l > lc, aut « 1). This in turn means that the length scale lc distinctly points out the UV/IR mixing property of the non-local theory under consideration. We have carried out the holographic study of entanglement entropy for each of these domains by employing both analytical and numerical techniques. The broken Lorentz symmetry induced by noncommutativity has motivated us to redefine the entropic c-function. We have obtained the noncommutative correction to the c-function upto leading order in the noncommutative parameter. We have also looked at the behaviour of this quantity over all the domains of the theory. We then move on to compute the minimal cross-section area of the entanglement wedge by considering two dis- joint subsystems A and B. On the basis of EP = EW duality, this leads to the holographic computation of the entanglement of purification. The correlation between two subsystems, namely, the holographic mutual information I(A : B) has also been computed. Moreover, the computations of EW and I(A : B) has been done for each of the domains in the theory. We have then briefly discussed the effect of the UV cut-off on the IR behaviours of these quantities. Finally, we consider a black hole geometry with a noncommutative parameter and study the influence of both noncommutativity and finite temperature on the various measures of quantum entanglement.

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“…Recently, the informational quantities have been explored for holographic dual field theory with Lifshitz symmetry; see Refs. [59][60][61][62][63] and references therein. However, most of these studies focused only on the HEE or MI in the background with zero charge density, and there have been few investigations on the informational quantities at finite density, especially the EoP.…”

Section: S A∪c S A∪c = S B + S A∪b∪cmentioning

confidence: 99%

Informational properties of holographic Lifshitz field theory *

Gong

Liu

et al. 2021

Chinese Phys. C

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In this paper, we explore the properties of holographic entanglement entropy (HEE), mutual information (MI) and entanglement of purification (EoP) in holographic Lifshitz theory. These informational quantities exhibit some universal properties of holographic dual field theory. For most configuration parameters and temperatures, these informational quantities change monotonically with the Lifshitz dynamical critical exponent z. However, we also observe some non-monotonic behaviors for these informational quantities in some specific spaces of configuration parameters and temperatures. A particularly interesting phenomenon is that a dome-shaped diagram emerges in the behavior of MI vs z, and correspondingly a trapezoid-shaped profile appears in that of EoP vs z. This means that for some specific configuration parameters and temperatures, the system measured in terms of MI and EoP is entangled only in a certain intermediate range of z.

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Holographic information theoretic quantities for Lifshitz black hole

Cited by 5 publications

References 58 publications

Holographic study of entanglement and complexity for mixed states

Holographic study of entanglement and complexity for mixed states

Entanglement wedge cross-section for noncommutative Yang-Mills theory

Informational properties of holographic Lifshitz field theory *

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