Abstract

Multipartite nonlocality is a measure of multipartite quantum correlations. In this paper, we investigate multipartite nonlocality in a spin-\(\frac{1}{2}\) XXZ model on a one-dimensional (1D) infinite-size zigzag lattice. In the ground states, the model can undergo topological-type quantum phase transitions (QPTs) between a singlet dimer (SD) phase and an even-parity dimer (ED) phase. Two nonlocality measures \({\mathcal {S}}_o\) (defined on the odd-bond subchains) and \({\mathcal {S}}_e\) (defined on the even-bond subchains) are used to characterize these topological-type QPTs. Both measures show some kinds of singularity (i.e., a discontinuity of the measure or the divergence of its derivative) in the QPTs. Furthermore, in the SD phase and in the vicinity of critical regions, \({\mathcal {S}}_o\) is relatively large, and in most regions of the ED phase, \({\mathcal {S}}_o\) is nearly zero. Thus, similar to order parameters in traditional phase transitions, \({\mathcal {S}}_o\) is an effective physical quantity to characterize these topological-type QPTs. Scaling behavior of the nonlocality measure is also discussed.

Graphical abstract

中文翻译：

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锯齿形晶格上自旋 1/2 XXZ 模型中的多部非定域性和拓扑量子相变

摘要

多方非局域性是多方量子相关性的度量。在本文中，我们研究了一维 (1D) 无限尺寸锯齿形晶格上的自旋\(\frac{1}{2}\) XXZ 模型中的多部非局域性。在基态中，该模型可以在单重态二聚体 (SD) 相和偶校验二聚体 (ED) 相之间经历拓扑型量子相变 (QPT)。两个非局部性度量\({\mathcal {S}}_o\)（定义在奇数键子链上）和\({\mathcal {S}}_e\)（在偶键子链上定义）用于表征这些拓扑类型的 QPT。两种测量都显示了 QPT 中的某种奇异性（即测量的不连续性或其导数的发散）。此外，在 SD 阶段和关键区域附近，\({\mathcal {S}}_o\)比较大，在 ED 阶段的大部分区域，\({\mathcal {S}}_o\ )几乎为零。因此，与传统相变中的阶参数类似，\({\mathcal {S}}_o\)是表征这些拓扑型 QPT 的有效物理量。还讨论了非局部性度量的缩放行为。

图形概要