Abstract

The behavior of the bipartite entanglement and multipartite quantum correlations for two dimensional square lattice of Heisenberg XY model with Dzyaloshinskii–Moriya (DM) interaction is studied in the framework of the quantum renormalization group (QRG) method. The analytical results are produced for the renormalized control parameters and a phase diagram is obtained for the model which shows the stable and unstable fix points corresponding to different phases. Concurrence and global quantum discord (GQD) are the quantifiers for the study of entanglement and quantum correlations respectively which are influenced in a different manner by the control parameters anisotropy γ and the DM interaction D. However, the behavior of the quantifiers at the critical point captures the quantum phase transition (QPT) described by the divergence of their first derivative with respect to anisotropy. It is found that the DM interactions among the spins try to recover the entanglement which is more prominent for the multipartite case. GQD is a more suitable candidate as it can describe the multipartite quantum correlations present among many spins (>2) in higher dimensions. Unlike the monogamy in entanglement the quantum correlations increase with the increasing number of the interacting spins.

Graphical abstract

中文翻译：

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Dzyaloshinskii-Moriya相互作用的二维XY模型中的纠缠和多方量子相关

摘要

在量子重归一化群（QRG）方法的框架下，研究了具有Dzyaloshinskii-Moriya（DM）相互作用的海森堡XY模型的二维方格的两方纠缠和多方量子相关性。对重新标准化的控制参数产生了分析结果，并为模型获得了一个相图，该相图显示了对应于不同相的稳定和不稳定的固定点。并发和全局量子失调（GQD）分别是纠缠和量子相关性研究的量词，它们分别受控制参数各向异性γ和DM交互作用D的不同影响。。但是，量词在临界点的行为捕获了由其一阶导数相对于各向异性的发散所描述的量子相变（QPT）。发现自旋之间的DM相互作用试图恢复纠缠，这对于多部分情况更为突出。GQD是更合适的候选者，因为它可以描述更高维数中许多自旋（> 2）之间存在的多部分量子相关性。与纠缠中的一夫一妻制不同，量子相关性随着相互作用的自旋数目的增加而增加。

图形概要