论文标题
高度纠缠的旋转链和2D量子重力
Highly entangled spin chains and 2D quantum gravity
论文作者
论文摘要
Motzkin和Fredkin自旋链显示出大量的纠缠缩放，作为音量的平方根，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密集研究，以揭示量子纠缠的新特征。作为对系统的研究，我们引入了具有所谓的ABAB相互作用的大N基质模型，其中相关函数重现了树和平面Feynman图中的纠缠缩放。包含环图自然定义了Motzkin和Fredkin自旋链的扩展。大N处的整个环效应的贡献使能力的增长3/2（具有对数校正），更远，超出了平方根的缩放。循环贡献提供了波动的二维散装几何形状，并且纠缠的增强被理解为量子重力的效果。
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.
