Correlations and entanglement in quantum critical bilayer and necklace XY models
Correlations and entanglement in quantum critical bilayer and necklace XY models
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DOI：
10.1103/physrevb.92.125120
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发表时间：
2014-11
影响因子：
3.7
通讯作者：
J. Helmes;S. Wessel
中科院分区：
文献类型：
--
作者：
J. Helmes;S. Wessel
基于有限环面和不同子区域形状的量子蒙特卡罗模拟，我们分析了二维方晶格双层和项链晶格上自旋半XY模型的临界性质和量子临界点处的纠缠尺度。对于这两个模型，发现横向交错自旋结构因子的有限尺寸缩放符合双分量三维${\ensuremath{\phi}}^{4}$理论所描述的量子临界点。在两个模型中，在子系统边界没有角的情况下，第二个R\ enyi纠缠熵都表现出面积律缩放，对于双层（项链）模型，面积律预因子分别为$0.0674(7)$ $[0.0664(4)]$。此外，${90}^{\ensuremath{\circ}}$角的存在导致在两个模型中都有一个可加的对数项。我们估计$\ensuremath{-}0.010(2)$ $[\ensuremath{-}0.009(2)]$由于每个${90}^{\ensuremath{\circ}}$角对双层（项链）模型的对数校正的贡献$ $[\ensuremath{-}0.009(2)]$，并将我们的发现与最近的数值链接簇计算和相关模型的序列展开结果进行比较。
We analyze the critical properties and the entanglement scaling at the quantum critical points of the spin-half XY model on a two-dimensional square-lattice bilayer and necklace lattice, based on quantum Monte Carlo simulations on finite tori and for different subregion shapes. For both models, the finite-size scaling of the transverse staggered spin structure factor is found in accord with a quantum critical point described by the two-component, three-dimensional ${\ensuremath{\phi}}^{4}$ theory. The second R\'enyi entanglement entropy in the absence of corners along the subsystem boundary exhibits area-law scaling in both models, with an area-law prefactor of $0.0674(7)$ $[0.0664(4)]$ for the bilayer (necklace) model, respectively. Furthermore, the presence of ${90}^{\ensuremath{\circ}}$ corners leads to an additive logarithmic term in both models. We estimate a contribution of $\ensuremath{-}0.010(2)$ $[\ensuremath{-}0.009(2)]$ due to each ${90}^{\ensuremath{\circ}}$ corner to the logarithmic correction for the bilayer (necklace) model, and compare our findings to recent numerical linked-cluster calculations and series expansion results on related models.