通过纠缠表面上的涌现序表征混合态中的长程纠缠
Characterizing Long-Range Entanglement in a Mixed State Through an Emergent Order on the Entangling Surface
AI总结：
本文通过建立纠缠负性度与纠缠二分表面上涌现的对称性保护拓扑序之间的联系，揭示了有限温度拓扑序中长程纠缠的普适模式及其对热涨落的稳定性。
摘要：
非零温度下的拓扑有序物质相被推测表现出长程纠缠的普适模式，这些模式可以通过称为纠缠负性度的混合态纠缠度量来检测。我们表明，某些拓扑序中的纠缠负性度可以通过纠缠二分表面上局域的涌现对称性保护拓扑（SPT）序的性质来理解。这种联系导致了对（i）诊断有限温度拓扑序的纠缠负性度的普适贡献，以及（ii）在热涨落最终破坏二分表面上的长程纠缠的某些相变中纠缠负性度行为的理解。在这种对应关系中，有限温度拓扑序中的纠缠普适模式与涌现SPT序对对称性破缺场的稳定性有关。由高形式对称性保护的SPT序——例如，在$d=4$空间维度的$\mathbb{Z}_{2}$拓扑序的纠缠负性度描述中出现——即使在弱对称性破缺扰动存在下也保持鲁棒，导致某些拓扑序在非零温度下仍具有长程纠缠。
英文摘要：
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.
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