高维AdS黑洞中Born-Infeld电动力学的纠缠熵探析

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本文主要探讨了在高维Anti-de Sitter (AdS)黑洞背景下，Born-Infeld (BI)电动力学对于全息金属/超导体模型中的纠缠熵的影响。BI电动力学是一种非线性的电动力学理论，它在经典电磁理论的基础上引入了电场强度的上限，这使得在强电场区域，电场强度不再无限增长，从而避免了经典电动力学中的某些问题。在高维AdS空间中，作者研究了一个具有BI电磁场的全息模型，这一模型被认为是对量子引力理论中的AdS/CFT对应关系的一种数学描述。全息纠缠熵是量子信息理论中的一个重要概念，它反映了系统的局部度量与全局状态之间的关系，尤其是在黑洞背景下的信息保真度和量子态的复杂性。研究发现，纠缠熵在金属相中随着BI因子的增大而减小，这是因为BI的非线性特性降低了标量冷凝的形成，这是一种在金属向超导转变过程中的关键现象。相反，在冷凝相中，纠缠熵表现出单调递增的趋势，这强化了BI电磁场对相变过程的调控作用，即随着非线性的增强，相变的敏感性也增加。此外，作者还关注了子系统宽度对全息纠缠熵的影响。子系统宽度通常代表了系统分割的精细程度，研究结果显示，当子系统宽度增大时，纠缠熵也随之增加，这表明更大的子系统规模可能揭示出更复杂的量子纠缠结构。总结来说，这篇论文通过深入分析BI电动力学对高维AdS黑洞时空下全息金属/超导体模型的纠缠熵影响，提供了新的视角来理解相变行为，特别是相变点和相变顺序的探测。这些发现不仅深化了我们对量子信息在AdS/CFT框架下的理解，也为未来的量子材料和量子信息处理技术提供了理论支持。

Eur. Phys. J. C (2019) 79:148

https://doi.org/10.1140/epjc/s10052-019-6643-5

Regular Article - Theoretical Physics

Holographic entanglement entropy with Born–Infeld

electrodynamics in higher dimensional AdS black hole spacetime

Weiping Yao

, Wenqing Zha

, Qiannan An

, Jiliang Jing

2,a

Department of electrical engineering, Liupanshui Normal University, Liupanshui 553004, Guizhou, People’s Republic of China

Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic

Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, Hunan, People’s Republic of China

Received: 8 January 2019 / Accepted: 3 February 2019 / Published online: 19 February 2019

Abstract We examine the entanglement entropy in higher

dimensional holographic metal/superconductor model with

Born–Infeld (BI) electrodynamics. We note that the entan-

glement entropy is still a powerful tool to probe the critical

phase transition point and the order of the phase transition

in higher dimensional AdS spacetime. Due to the presence

of the BI electromagnetic ﬁeld, the formation of the scalar

condensation becomes harder. For both operators O

 and

O

−

, we show that the entanglement entropy in the metal

phase decreases as the BI factor increases, but in condensa-

tion phase the entanglement entropy increases monotonically

for stronger nonlinearity of BI electromagnetic ﬁeld. Further-

more, we also study the inﬂuence of the width of the subsys-

tem on the holographic entanglement entropy and observe

that with the increase of the width the entanglement entropy

increases.

1 Introduction

The entanglement entropy serves as a key quantity to mea-

sure how the subsystem and its complement are correlated

[1]. In strongly coupled system, the entanglement entropy is

expected to be a useful tool to keep track of the degree of free-

dom while other traditional methods might not be available.

However, the calculation of entanglement entropy is usually

a not easy task except for the case in 1+1 dimensions. In the

spirit of the anti-de Sitter/conformal ﬁeld theory (AdS/CFT)

correspondence [2–4], Ryu and Takayanagi have provided a

holographic proposal to compute the entanglement entropy in

[5,6]. It states that the entanglement entropy of a d+1 dimen-

sional CFT at strong coupling can be investigated from a

weakly coupled gravity dual characterized by an asymptot-

ically AdS

+ 2 spacetime. With this elegant approach, the

e-mail: jljing@hunnu.edu.cn

holographic entanglement entropy is widely used to study

properties of phase transitions in holographic superconduc-

tor models [7–12]. The behavior of the entanglement entropy

in metal/superconductor phase transition was studied in [13]

and observed that the entanglement entropy is lower in the

superconductor phase than in the normal phase. In the insu-

lator/superconductor model, the non-monotonic behavior of

the entanglement entropy was found in Ref. [14]. Then, the

study of entanglement entropy was also extended to other

various holographic superconductors applications [15–26].

The purpose of this paper is to study further the behaviors

of the holographic entanglement entropy for metal/super-

conductor model with BI electrodynamics in higher dimen-

sional AdS spacetime. On the one hand, the motivations for

studying the entanglement entropy in higher dimensional

black hole spacetime comes from the string theory which

contains gravity and requires more than four dimensions

[27,28]. Furthermore, as mathematical objects, black hole

spacetimes are among the most important Lorentzian Ricci-

ﬂat manifolds in any dimension [29]. On the other hand,

the BI electrodynamics [30] introduced in 1930s by Born

and Infeld to obtain a classical theory of charged particles

with ﬁnite self-energy, is the only possible non-linear version

of electrodynamics which is invariant under electromagnetic

duality transformations and has been a focus for these years

since most physical systems are inherently nonlinear to some

extent [31–38]. The Lagrangian of the BI gauge ﬁeld and its

expression is given by

⎛

⎝

1 −



1 +

μν

⎞

⎠

, (1)

where F

μν

= ∂

− ∂

is the strength of the BI elec-

trodynamic ﬁeld. b is the BI coupling parameter. In the limit

b → 0, the BI ﬁeld will reduce to the Maxwell ﬁeld. It is

123

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