标题： 探测磁性稀土簇中的非局域关联 显示英文标题

标题： Probing nonlocal correlations in magnetic rare-earth clusters

摘要： 理解并量化纠缠熵对于表征驱动各种系统中现象的量子行为至关重要。稀土自旋复合物因其独特的磁性特性，为探索这些非局域关联提供了肥沃的土壤。在本工作中，我们研究了沉积在Au(111)基底上的Eu$^{2+}$离子，使用由第一性原理计算参数化的海森堡哈密顿量来模拟大自旋矩的有限团簇。我们的分析揭示了微分电导谱中的结构与双部分子系统冯·诺依曼纠缠熵变化之间的一一对应关系，该关系受探针离子间距和施加磁场的影响。导电谱中的独特编织模式被证明对应于纠缠熵的分步变化，为研究量子关联提供了一条新途径。这些结果为实验探测和控制基于镧系元素的系统中的纠缠奠定了基础，具有在量子技术中的潜在应用。 显示英文摘要

摘要： Understanding and quantifying entanglement entropy is crucial to characterize the quantum behaviors that drive phenomena in a variety of systems. Rare-earth spin complexes, with their unique magnetic properties, provide fertile ground for exploring these nonlocal correlations. In this work, we study Eu$^{2+}$ ions deposited on a Au(111) substrate, modeling finite clusters of large spin-moments using a Heisenberg Hamiltonian parameterized by first-principles calculations. Our analysis reveals a one-to-one correspondence between structures in the differential conductance profiles and changes in the von Neumann entanglement entropy of bipartite subsystems, influenced by probe-ion separation and applied magnetic fields. Distinct braiding patterns in the conductance profiles are shown to correspond to stepwise changes in the entanglement entropy, providing a new avenue for investigating quantum correlations. These results establish a foundation for experimentally probing and controlling entanglement in lanthanide-based systems, with potential applications in quantum technologies.