发表机构
University of Siena; INFN Sezione di Perugia（锡耶纳大学; 佩鲁贾意大利国家核物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用纠缠距离解析了Katz加权图态中纠缠的生成，揭示了弱与强传播区域的动力学特征，并连接了纠缠动力学与复杂网络的谱结构。
AI 中文摘要
我们研究了由底层网络的Katz核所控制的非局域Ising相互作用的图上的量子态的纠缠动力学。该相互作用模式在物理上由一个在同一图上传播的有能隙的费米子媒介所激发，对其的微扰消除产生了一个有效的Katz加权Ising哈密顿量。利用纠缠距离，我们推导了从初始可分离态产生的纠缠的精确解析表达式，并将其应用于代表性的确定性图族。然后，我们刻画了不同传播区域中的动力学。在弱Katz区域，动力学允许一个系统的团展开，其中三角形在一阶出现，而四环、局部度结构和重叠三角形在二阶出现。在强传播区域，相互作用则主要由主邻接模式及其特征向量的局域化性质所主导。对于Erdős–Rényi图，弱传播展开可以解析地平均，揭示了稀疏区域中局部树状的贡献以及稠密区域中纠缠距离密度的饱和。我们的结果将纠缠动力学与复杂网络的基于游走和谱的结构联系起来。
英文摘要
We investigate the entanglement dynamics of quantum states defined on graphs with non-local Ising interactions governed by the Katz kernel of the underlying network. The interaction pattern is physically motivated by a gapped fermionic mediator propagating on the same graph, whose perturbative elimination yields an effective Katz-weighted Ising Hamiltonian. Using the Entanglement Distance, we derive an exact analytical expression for the entanglement generated from an initially separable state and apply it to representative deterministic graph families. We then characterize the dynamics in different propagation regimes. In the weak-Katz regime, the dynamics admits a systematic motif expansion with triangles entering at first order order and four-cycles, local degree structure, and overlappin triangles appearing at second order. In the strong-propagation regime, the interaction is instead dominated by the principal adjacency mode and by the localization properties of its eigenvector. For Erdős--Rényi graphs, the weak-propagation expansion can be averaged analytically, revealing a locally tree-like contribution in the sparse regime and saturation of the Entanglement Distance density in the dense regime. Our results connect entanglement dynamics with both the walk-based and spectral structure of complex networks.
Comments11 pages, 6 figures
