The European Physical Journal B ( IF 1.6 ) Pub Date : 2021-07-12 , DOI: 10.1140/epjb/s10051-021-00150-7 Zhao-Yu Sun 1 , Meng Li 1 , Hui-Xin Wen 1 , Hong-Guang Cheng 1 , Jian Xu 1 , Yan-Shan Chen 1
Abstract
Multipartite nonlocality, a measure of multipartite quantum correlations, is used to characterize topological quantum phase transitions (QPTs) in an infinite-size spin-1/2 two-leg Kitaev ladder model. First of all, the nonlocality measure \({\mathcal {S}}\) is singular at the critical points, thus these topological QPTs are accompanied by dramatic changes of multipartite quantum correlations. The influence of the inter-chain coupling upon multipartite nonlocality is also investigated. Furthermore, we carry out scaling analysis and find that the logarithm measure scales linearly as \(\log _2{\mathcal {S}}_n \sim {\mathcal {K}} n +b\), with n the length of the concerned subchain. It is clear that the slope \({\mathcal {K}}\) plays a central role in the large-n behavior of the nonlocality in the ladder. Especially, as n increases, we find the finite-size slope \({\mathcal {K}}_n\) converges slowly in the \(\varDelta _{x,y}\) phases which present non-local string orders, and quite rapidly in the \(\varDelta _0\) phase which does not present any string order. We figure out a clear picture to explain these different behaviors.
Graphic abstract
中文翻译:
自旋 1/2 双腿 Kitaev 阶梯中的多部分量子非局域性和拓扑量子相变
摘要
多部分非定域性是多部分量子相关性的一种度量,用于表征无限大小自旋 1/2 两腿 Kitaev 阶梯模型中的拓扑量子相变 (QPT)。首先,非局域性测度\({\mathcal {S}}\)在临界点是奇异的,因此这些拓扑 QPT 伴随着多方量子相关性的剧烈变化。还研究了链间耦合对多部分非局部性的影响。此外,我们进行了标度分析,发现对数度量线性标度为\(\log _2{\mathcal {S}}_n \sim {\mathcal {K}} n +b\),其中n为有关子链。很明显,斜率\({\mathcal {K}}\)在阶梯中非定域性的大n行为中起着核心作用。特别是,随着n 的增加,我们发现有限大小的斜率\({\mathcal {K}}_n\)在呈现非局部弦阶的\(\varDelta _{x,y}\)阶段缓慢收敛,并且在\(\varDelta _0\)阶段非常迅速,不存在任何字符串顺序。我们想出了一个清晰的图片来解释这些不同的行为。