Hyperbolic fracton model, subsystem symmetry, and holography
Hyperbolic fracton model, subsystem symmetry, and holography
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双曲分形模型、子系统对称性和全息术
DOI：
10.1103/physrevb.99.155126
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发表时间：
2019
影响因子：
3.7
通讯作者：
Yan Han
中科院分区：
文献类型：
--
作者：
Yan Han;Benton Owen;Jaubert L. D. C.;Shannon Nic;Yan Han
我们提出具有子系统对称性的分形模型可以作为全息原理的一类玩具模型。反德西特/共形场论对应关系作为全息术的具体构造的发现，以及随后的发展，包括子区域对偶和ryutakayanagi纠缠熵公式，彻底改变了我们对量子引力的理解，并为解决各种强耦合量子场论问题提供了强大的工具集。为了解开全息摄影的许多谜团，玩具模型会很有帮助。一个例子是全息张量网络，它阐明了反德西特空间中引力的量子纠错特性。在这项工作中，我们讨论了一个经典的玩具模型，具有子系统对称性和不动分数激励。我们证明了这种定义在双曲晶格上的模型满足全息对应的一些关键性质。建立了连通边界区域的正确子区域对偶性和Ryu-Takayanagi互信息公式。一个简单定义的黑洞的熵尺度就是它的视界面积。我们还讨论了更复杂的边界子区域的修正，模型的可能推广，以及与全息张量网络的比较。
We propose that the fracton models with subsystem symmetry can be a class of toy models for the holographic principle. The discovery of the anti–de Sitter/conformal field theory correspondence as a concrete construction of holography and the subsequent developments including the subregion duality and Ryu-Takayanagi formula of entanglement entropy have revolutionized our understanding of quantum gravity and provided powerful tool sets for solving various strongly coupled quantum field theory problems. To resolve many mysteries of holography, toy models can be very helpful. One example is the holographic tensor networks, which illuminate the quantum-error-correcting properties of gravity in the anti–de Sitter space. In this work we discuss a classical toy model featuring subsystem symmetries and immobile fracton excitations. We show that such a model defined on the hyperbolic lattice satisfies some key properties of the holographic correspondence. The correct subregion duality and Ryu-Takayanagi formula for mutual information are established for a connected boundary region. A naively defined black hole's entropy scales as its horizon area. We also present discussions on corrections for more complicated boundary subregions, the possible generalizations of the model, and a comparison with the holographic tensor networks.