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.

中文翻译：

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高度纠缠自旋链和二维量子引力

Motzkin 和 Fredkin 自旋链表现出非凡数量的纠缠缩放作为体积的平方根，这超出了普通临界系统中的对数缩放。敦促对这种自旋系统进行深入研究，以揭示量子纠缠的新特征。作为从不同角度对系统的研究，我们引入了具有所谓 ABAB 相互作用的大 N 矩阵模型，其中相关函数再现了树和平面费曼图中的纠缠缩放。包括循环图自然定义了 Motzkin 和 Fredkin 自旋链的扩展。来自大 N 的整个循环效应的贡献给出了 3/2 的幂的增长（使用对数校正），进一步超出了平方根缩放。循环贡献提供波动的二维体几何，