Holographic entanglement negativity and replica symmetry breaking
Holographic entanglement negativity and replica symmetry breaking
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DOI：
10.1007/jhep06(2021)024
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发表时间：
2021-06-03
影响因子：
5.4
通讯作者：
Walter, Michael
中科院分区：
文献类型：
--
作者：
Dong, Xi;Qi, Xiao-Liang;Walter, Michael
自从Ryu和Takayanagi的工作以来，量子纠缠和时空几何之间的深层联系已经被揭示出来。二分密度算符部分转置的负本征值是纠缠的一个有用的诊断。本文讨论了全息对偶中纠缠负性及其Renyi推广的性质。我们首先回顾了Renyi负性的定义，其中包含了常见的对数负性作为特例。然后，我们在随机张量网络模型中研究这些量，并严格推导出它们的大键维渐近。最后，我们研究了引力对偶的全息理论中的纠缠负性，我们发现Renyi负性通常由打破副本对称性的体解主导。从这些副本对称性破缺的解决方案，我们得到的Renyi负和他们的特殊限制，包括对数负的一般表达式。在固定面积状态下，这些一般表达式大大简化，并与我们在随机张量网络模型中的结果完全一致。这为进一步研究全息术中复制品对称性破缺的意义提供了一个具体的背景。
Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its Renyi generalizations in holographic duality. We first review the definition of the Renyi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Renyi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Renyi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.