标题： 双曲分形模型，子系统对称性与全息理论 II：对偶八顶点模型 显示英文标题

标题： Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model

摘要： 物质的分形子态的发现开启了一个令人兴奋的、 largely 未探索的多体物理领域。 某些分形子态与引力的相似性是一个引人入胜的特性。 在之前的工作 [H. Yan, Phys. Rev. B 99, 155126 (2019)] 中，我们已经证明了反德西特空间中的一个简单分形子模型满足几个主要的全息性质。 在本文的后续论文中，我们研究了与原模型对偶的八顶点模型。 对偶模型的优势在于能够形象地阐明互信息和子系统电荷，这有助于揭示它与其他各种主题在全息和分形子相研究中的联系。 在零温度下，对偶的八顶点模型是位线模型的一个离散实现，这是一个用于可视化全息的有力工具。 位线图像与子系统电荷相结合，可以对有限能量下体和边界之间的等距性进行定量描述，这也是全息的关键问题之一。 黑洞的微观自由度可以在这个图像中被识别出来，结果发现它们是在视界上非局部编码的。 八顶点模型被证明是非常有用的场所，以提高我们对双曲分形子模型作为全息理论的玩具模型的理解。 显示英文摘要

摘要： The discovery of fracton states of matter opens up an exciting, largely unexplored field of many-body physics. Certain fracton states' similarity to gravity is an intriguing property. In an earlier work [H. Yan, Phys. Rev. B 99, 155126 (2019)], we have demonstrated that a simple fracton model in anti-de Sitter space satisfies several major holographic properties. In this follow-up paper, we study the eight-vertex model dual to the original model. The dual model has the advantage of illuminating the mutual information and subsystem charges pictorially, which helps to reveal its connections to various other topics in the study of holography and fracton phases. At zero temperature, the dual eight-vertex model is a discrete realization of the bit-thread model, a powerful tool developed to visualize holography. The bit-thread picture combined with subsystem charges can give a quantitative account of the isometry between the bulk and the boundary at finite energy, which is also a key issue for holography. The black hole microscopic degrees of freedom can be identified in this picture, which turn out to be encoded non-locally on the horizon. The eight-vertex model proves to be a very helpful venue to improve our understanding of the hyperbolic fracton model as a toy model of holography.