高纠缠自旋链与二维量子引力
Highly entangled spin chains and 2D quantum gravity
摘要：
Motzkin和Fredkin自旋链表现出非常大的纠缠尺度作为体积的平方根，这超出了普通临界系统的对数尺度。对这种自旋系统的深入研究有助于揭示量子纠缠的新特性。作为对系统的另一种研究，我们引入了具有ABAB相互作用的大N矩阵模型，其中关联函数再现了树图和平面费曼图中的纠缠标度。包含循环图自然定义了Motzkin和Fredkin自旋链的扩展。在大N时，来自整个回路效应的贡献给出了3/2的幂的增长（具有对数校正），进一步超出平方根标度。环的贡献提供了波动的二维体几何，和纠缠的增强被理解为量子引力的效果。
英文摘要：
Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal novel features of quantum entanglement. As a study of the systems from a different viewpoint, we introduce large-N matrix models with so-called ABAB interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams. Including loop diagrams naturally defines an extension of the Motzkin and Fredkin spin chains. Contribution from the whole loop effects at large N gives the growth of the power of 3/2 (with logarithmic correction), further beyond the square-root scaling. The loop contribution provides fluctuating two-dimensional bulk geometry, and the enhancement of the entanglement is understood as an effect of quantum gravity.
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