Flat entanglement spectra in fixed-area states of quantum gravity
Flat entanglement spectra in fixed-area states of quantum gravity
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DOI：
10.1007/jhep10(2019)240
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发表时间：
2019-10-24
影响因子：
5.4
通讯作者：
Marolf, Donald
中科院分区：
文献类型：
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作者：
Dong, Xi;Harlow, Daniel;Marolf, Donald
我们利用Einstein-Hilbert引力路径积分研究了首阶为O（1/G）的引力纠缠。我们认为，由欧几里德路径积分制备的半经典态具有这样的性质，即在引力微扰理论中，将它们投影到Ryu-Takayanagi或Hubeny-Rangamani-Takayanagi表面具有确定面积的子空间上，得到具有该阶平坦纠缠谱的态。这意味着约化密度矩阵可以近似为与单位元成比例，其Renyi熵Sn在该阶独立于n。在更一般的状态下，Sn的n依赖性则由RT/HRT面积上的总和产生，RT/HRT面积通常由每个n的该面积的不同值决定。这提供了引力纠缠的一个简单的图像，支持全息系统和张量网络模型之间的联系，澄清了在全息的量子纠错描述中出现的代数中心的体解释，并加强了Jafferis，Lewkowycz，Maldacena和Suh描述的体和边界模块哈密顿之间的联系。
We use the Einstein-Hilbert gravitational path integral to investigate gravita- tional entanglement at leading order O(1/G). We argue that semiclassical states prepared by a Euclidean path integral have the property that projecting them onto a subspace in which the Ryu-Takayanagi or Hubeny-Rangamani-Takayanagi surface has definite area gives a state with a flat entanglement spectrum at this order in gravitational perturbation theory. This means that the reduced density matrix can be approximated as proportional to the identity to the extent that its Renyi entropies Sn are independent of n at this order. The n-dependence of Sn in more general states then arises from sums over the RT/HRT- area, which are generally dominated by different values of this area for each n. This provides a simple picture of gravitational entanglement, bolsters the connection between holographic systems and tensor network models, clarifies the bulk interpretation of alge- braic centers which arise in the quantum error-correcting description of holography, and strengthens the connection between bulk and boundary modular Hamiltonians described by Jafferis, Lewkowycz, Maldacena, and Suh.