AI 中文总结
通过图论方法研究伊辛自旋网络中的可积-混沌转变与信息加扰，发现长程耦合和异质度分布加速量子信息传播，非局域相互作用驱动信息深度加扰，并建立了网络拓扑与信息、算符及谱诊断的统一框架。
AI 中文摘要
我们通过图论公式研究伊辛自旋网络中的可积-混沌转变和信息加扰。将自旋建模为顶点，并通过路径、Erdős–Rényi和Watts–Strogatz拓扑中的邻接矩阵描述相互作用，我们证明长程耦合和异质度分布极大地加速了量子信息传播。哈密顿量包含局域和归一化的非局域相互作用；调节非局域耦合和场异质性驱动可积性破缺。为量化加扰，我们采用二分互信息和三分信息。增加非局域相互作用使三分信息趋于大的负值，标志着深度信息加扰。时序外关联子（OTOC）呈现指数早期增长，产生量子李雅普诺夫指数，其随控制混沌区的参数系统变化。作为补充，Krylov复杂度揭示了混沌相中算符的快速增长，与OTOC和互信息动力学同步。谱方面，转变表现为从泊松到Wigner–Dyson能级间距统计的转移。谱形状因子（SFF）呈现特征性的斜率-下降-斜坡-平台结构，从而提取Thouless时间和Heisenberg时间。关键的是，减小的Thouless时间与加速的信息和算符加扰强相关。最终，这项工作建立了连接网络拓扑与信息论、算符和谱诊断的统一框架，为量子多体系统中的热化和非平衡动力学提供了深刻见解。
英文摘要
We investigate the integrability-to-chaos transition and information scrambling in Ising spin networks via a graph-theoretic formulation. Modeling spins as vertices and interactions as edges encoded by adjacency matrices across path, Erdos-Renyi, and Watts-Strogatz topologies, we demonstrate that long-range couplings and heterogeneous degree distributions markedly accelerate quantum information propagation. The Hamiltonian comprises local and normalized non-local interactions; tuning the non-local coupling and field heterogeneity drives integrability breaking. To quantify scrambling, we employ bipartite mutual and tripartite information. Increasing non-local interactions drives tripartite information to large negative values, signaling deep information scrambling. The squared commutators constructed from out-of-time-order correlators (OTOCs) exhibit early-time exponential growth; equivalently, the OTOC four-point functions themselves decay exponentially, yielding quantum Lyapunov exponents that scale systematically with parameters governing the chaotic regime. Complementing this, Krylov complexity reveals rapid operator growth in the chaotic phase, synchronizing with OTOC and mutual information dynamics. Spectrally, the transition manifests as a shift from Poissonian to Wigner-Dyson level spacing statistics. The spectral form factor (SFF) exhibits the characteristic slope-dip-ramp-plateau structure, enabling the extraction of Thouless and Heisenberg times. Crucially, a reduced Thouless time strongly correlates with accelerated information and operator scrambling. Ultimately, this work establishes a unified framework bridging network topology with information-theoretic, operator, and spectral diagnostics, offering insights into thermalization and non-equilibrium dynamics in quantum many-body systems.
Comments33 pages,11 figures, References added, typo fixed
