论文标题
通过在纠缠表面上的紧急顺序在混合状态下以远程纠缠来表征远程纠缠
Characterizing Long-Range Entanglement in a Mixed State Through an Emergent Order on the Entangling Surface
论文作者
论文摘要
在非零温度下拓扑阶的物质阶段猜想表现出长期纠缠的通用模式，可以通过称为纠缠负性的混合状态纠缠措施来检测。我们表明，可以通过固定在纠缠两部分中的紧急对称性保护拓扑（SPT）的属性来理解某些拓扑顺序的纠缠负性。这种连接导致对（$ i $）对纠缠负面的（诊断有限的拓扑顺序）的（$ i $）普遍贡献的理解，以及（$ ii $）在某些相变的某些相变的纠缠负效率的行为，在这些相过渡中，热波动最终破坏了整个两部分表面的远程纠缠。在此对应关系中，有限温度拓扑顺序中的纠缠的通用模式与紧急SPT秩序与对称性领域的稳定性有关。 SPT订单受到更高形式对称性保护的订单 - 例如，在描述$ \ Mathbb {z} _ {2} $ d = 4 $ d = 4 $ d = 4 $ d = 4 $ d = 4 $ d = 4 $ d = 4 $ depogical order的纠缠负态性的描述中 - 即使在不符合对称性的扰动方面，也可以在不范围的情况下进行稳定的范围，从而导致了长距离范围内的范围，在不范围内进行了良好的范围。
Topologically-ordered phases of matter at non-zero temperature are conjectured to exhibit universal patterns of long-range entanglement which may be detected by a mixed-state entanglement measure known as entanglement negativity. We show that the entanglement negativity in certain topological orders can be understood through the properties of an emergent symmetry-protected topological (SPT) order which is localized on the entanglement bipartition. This connection leads to an understanding of ($i$) universal contributions to the entanglement negativity which diagnose finite-temperature topological order, and ($ii$) the behavior of the entanglement negativity across certain phase transitions in which thermal fluctuations eventually destroy long-range entanglement across the bipartition surface. Within this correspondence, the universal patterns of entanglement in the finite-temperature topological order are related to the stability of an emergent SPT order against a symmetry-breaking field. SPT orders protected by higher-form symmetries -- which arise, for example, in the description of the entanglement negativity for $\mathbb{Z}_{2}$ topological order in $d=4$ spatial dimensions -- remain robust even in the presence of a weak symmetry-breaking perturbation, leading to long-range entanglement at non-zero temperature for certain topological orders.
