高阶空间分离关联与长程横场伊辛模型中的量子魔法

中文摘要 AI 辅助

长程相互作用量子系统展现出超越最近邻体系的有趣现象。此类相互作用能够触及相距更远的粒子，并改变多体关联的行为。在此，我们分析了具有以$1/r^α$幂律衰减相互作用的反铁磁长程相互作用横场伊辛模型中这些关联的结构。我们考察了基态在临界点附近、针对不同相互作用指数$α$和固定系统尺寸的、与基无关的总多体关联（称为扇区长度$S_k$）的空间行为。这些关联函数已被证明能够指示纠缠以及局部实在模型的存在，从而使我们能够对该系统中的贝尔非局域性和纠缠做出论断。我们进一步在非稳定子性（通常称为量子魔法）的背景下研究它们，量子魔法蕴含了其经典可模拟性及对量子计算有用性的信息。我们评估了临界性附近及之外的R{é}nyi稳定子熵，并表明对于所有考察的系统尺寸，累积魔法（直至临界点）随$α$的增加而增加。我们的结果为长程相互作用、可观测的非经典现象及其经典可模拟性之间的相互作用提供了新的见解。

英文摘要

Long-range interacting quantum systems exhibit interesting phenomena beyond the nearest-neighbours regime. Such interactions can reach further separated particles and change the behaviour of many-body correlations. Here, we analyse their structure in the antiferromagnetic long-range interaction transverse field Ising model with power-law interactions decaying as $1/r^α$. We examine the spatial behaviour of basis-independent total multipartite correlations, called sector lengths $S_k$, of its ground state in the vicinity of critical points for different interaction exponents $α$ and fixed system size. These correlation functions were shown to indicate entanglement and the existence of local realistic models, allowing us to make claims about the Bell nonlocality and entanglement in the system. We further investigate them in the context of non-stabiliserness, often referred to as quantum magic, which holds information on their classical simulability and usefulness for quantum computation. We evaluate R{é}nyi stabiliser entropy near and outside the criticality and show that cumulative magic, up to the critical point, increases with $α$ for all of the examined system sizes. Our results provide new insights into the interplay between the long-range interactions, observable non-classical phenomena and their classical simulability.

发表机构

• National University of Singapore（新加坡国立大学）
• University of Gdańsk（格但斯克大学）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

comments would be much appreciated, 7 pages, 5 figures