Entanglement of Skeletal Regions,Physical Review Letters

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Entanglement of Skeletal Regions
Physical Review Letters ( IF 8.1 ) Pub Date : 2022-06-16 , DOI: 10.1103/physrevlett.128.240502
Clément Berthiere _{1,

2} , William Witczak-Krempa _{1,

2}

Affiliation

The entanglement entropy (EE) encodes key properties of quantum many-body systems. It is usually calculated for subregions of finite volume (or area in 2D). Here, we study the EE of skeletal regions that have no volume, such as a line in 2D. We show that skeletal entanglement displays new behavior compared with its bulk counterpart, and leads to distinct universal quantities. We provide nonperturbative bounds for the skeletal area-law coefficient of a large family of quantum states. We then explore skeletal scaling for the toric code, conformal bosons and Dirac fermions, Lifshitz critical points, and Fermi liquids. We discover signatures including skeletal topological EE, novel corner terms, and strict area-law scaling for metals. These findings suggest that skeletal entropy serves as a measure for the range of entanglement. Finally, we outline open questions relating to other systems and measures such as the logarithmic negativity.

中文翻译：

骨骼区域的纠缠

纠缠熵 (EE) 编码了量子多体系统的关键特性。它通常是针对有限体积（或二维面积）的子区域计算的。在这里，我们研究了没有骨骼区域的 EE体积，例如 2D 中的一条线。我们表明，与大块对应物相比，骨骼纠缠显示出新的行为，并导致不同的普遍量。我们为一大族量子态的骨架面积定律系数提供了非微扰界限。然后，我们探索复曲面代码、保形玻色子和狄拉克费米子、Lifshitz 临界点和费米液体的骨架缩放。我们发现了包括骨架拓扑 EE、新颖的角项和金属的严格面积定律缩放在内的特征。这些发现表明，骨骼熵可以作为纠缠范围的衡量标准。最后，我们概述了与其他系统和度量相关的开放性问题，例如对数负性。

更新日期：2022-06-16

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