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理论物理通讯：英文版

Quantum Correlations in Infinite XY Spin-1/2 Chains and Quantum Phase Transition

谭小东, 黄寿胜, 金柏琪

Published Feb 15, 2013• 0 citations
OpenAlex

Abstract

我们检验量不一致( QD )和纠纷(同时发生，文件结束和否定性)的能力检测为 XY 模型联系到量阶段转变( QPT )的批评的点，即，有在零温度的三纺纱的相互作用的各向同性的 XY 模型，并且在在有限温度的横向的磁场 h 的各向异性的 XY 模型。为零温度的盒子，我们发现纠纷和 QD 能为这二个模型聚焦 QPT 的批评的点。而且， QD 对距离 M 为各向异性的 XY 模型展出量关联的远程的行为，当纠纷是 short-ranged 时。为有限温度的盒子，我们发现那否定性与同时发生有一样的行为在或在转变点附近。而且，为各向异性的 XY 模型的 QD 能甚至当一个磁场不在时与温度增加。

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基于矩阵乘积态表述的无限时间演化块算法, 研究了具有x、y与z三个自旋方向的轨道自由度和轨 道序竞争的量子罗盘自旋链模型. 为了刻画该模型的量子相和相变, 计算了基态能量、局域序参量、 弦关联序参量、临界指数、冯诺依曼熵、有限纠缠标度和中心荷. 结果表明：该量子基态相图由条纹 反铁磁相、反铁磁相、单调奇数Haldane 相和振荡奇数Haldane相构成. 从条纹反铁磁相到反铁磁相, 以及从单调奇数Haldane相到振荡奇数Haldane相发生了非连续相变; 从振荡奇数Haldane相到条纹反铁 磁相, 以及从反铁磁相到单调奇数Haldane相发生了连续相变; 连续相变线和非连续相变线的交点是多 临界点. 此外, 连续相变点处的临界指数β = 1=8和中心荷c = 1=2表明连续相变的普适类属于Ising类. 由此揭示了该模型量子基态相图的本性, 对今后研究更高自旋以及更为复杂轨道序竞争的量子罗盘链 模型的量子相与相变具有一定借鉴与参考意义.

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我们检验量不一致( QD )和纠纷(同时发生，文件结束和否定性)的能力检测为 XY 模型联系到量阶段转变( QPT )的批评的点，即，有在零温度的三纺纱的相互作用的各向同性的 XY 模型，并且在在有限温度的横向的磁场 h 的各向异性的 XY 模型。为零温度的盒子，我们发现纠纷和 QD 能为这二个模型聚焦 QPT 的批评的点。而且， QD 对距离 M 为各向异性的 XY 模型展出量关联的远程的行为，当纠纷是 short-ranged 时。为有限温度的盒子，我们发现那否定性与同时发生有一样的行为在或在转变点附近。而且，为各向异性的 XY 模型的 QD 能甚至当一个磁场不在时与温度增加。
量关联由量不一致(QD ) 测量了，导致测量的距离(中间) ，并且在 two-qubit Heisenberg XY 旋转链的量不一致(GMQD ) 的几何措施被调查。DM 相互作用的效果并且在三关联上各向异性被考虑。为 two-qubit 状态的各种各样的关联措施的特征被比较。增加的 Dz 增加 QD，中间并且 GMQD 单调地当时增加的 anisotropy 增加和减少 QD 和 GMQD。三量关联在很高的温度总是是存在的。中间总是比 QD 大，但是在 QD 和 GMQD 之间没有明确的订。
We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.
Pairwise quantum discord (QD) and classical correlation (CC) are studied in the XY\mathit{XY}XY spin chain with three-spin interaction. We analyze their capability in detecting quantum phase transitions (QPTs) at both zero and finite temperatures and find that the pairwise QD of two neighboring spins is more reliable than that of any other distances in identifying QPTs. Both the QD and CC detect quantum critical points associated with first- and higher-order QPTs caused by field and three-spin interactions at finite temperatures. In addition, we find a different finite-size scaling behavior for QD from previous reports for the transverse field Ising case and show some interesting phenomena of QD and entanglement of formation for finite temperatures.
我们在场与矩阵产品在旋转链系统构造各种各样的量阶段转变(QPT ) 的一个新一般、简单得多的计划扎根了状态。由计划的使用，我们考虑一个种矩阵产品状态(MPS ) QPT 并且提供一个具体模型。我们也学习一种 QPT 出现的具体例子和表演的性质，由同等值的断绝的外观伴随了不在的块仅仅为同等值的物理看得见的、分叉的关联长度不在的块操作员，并且是转变点的固定的点是重正常化的一个孤立的中间联合的固定的点的另外的性质流动并且一半无限的链的纠纷熵是不连续的。[从作者抽象]
We study the quantum correlations in a spin-1/2 (qubit) and spin-1 (qutrit) Heisenberg XY model separately, based on quantum discord (QD) and measurement-induced disturbance (MID) respectively. We find the evidence of the first- and second-order quantum phase transition (QPT) in both spin-1/2 and spin-1 systems. The effect of the temperature, magnetic field and Dzyaloshinskii–Moriya (DM) interactions on QPT and quantum correlation are also investigated. Finally, we observed that the QD and MID are not only vigorous for higher spin systems but also more robust than entanglement.
基于矩阵乘积态表述的无限时间演化块算法, 研究了具有x、y与z三个自旋方向的轨道自由度和轨 道序竞争的量子罗盘自旋链模型. 为了刻画该模型的量子相和相变, 计算了基态能量、局域序参量、 弦关联序参量、临界指数、冯诺依曼熵、有限纠缠标度和中心荷. 结果表明：该量子基态相图由条纹 反铁磁相、反铁磁相、单调奇数Haldane 相和振荡奇数Haldane相构成. 从条纹反铁磁相到反铁磁相, 以及从单调奇数Haldane相到振荡奇数Haldane相发生了非连续相变; 从振荡奇数Haldane相到条纹反铁 磁相, 以及从反铁磁相到单调奇数Haldane相发生了连续相变; 连续相变线和非连续相变线的交点是多 临界点. 此外, 连续相变点处的临界指数β = 1=8和中心荷c = 1=2表明连续相变的普适类属于Ising类. 由此揭示了该模型量子基态相图的本性, 对今后研究更高自旋以及更为复杂轨道序竞争的量子罗盘链 模型的量子相与相变具有一定借鉴与参考意义.