AI 中文总结
该研究以海森堡XXZ模型等量子自旋链为对象，推导热赝熵实部与谱形状因子的精确关系，证实赝熵可诊断量子混沌，还推导了赝熵与谱复杂性的关联，可能与全息术相关。
AI 中文摘要
本研究针对量子自旋链（海森堡XXZ模型与混场伊辛模型），探究赝熵与谱动力学是否可作为量子混沌的诊断工具。首先推导了热赝熵实部与谱形状因子的精确关系，为赝熵呈现特征性的下降、对数上升及平台提供了证据，表明其探测混沌的具体方式。研究发现，赝熵虚部虽无法诊断混沌，但仍能提供实部无法获取的费希尔零点关键信息。对于XXZ链中的空间赝熵，发现其对数临界标度在可积与混沌区域均存在，且非正性猜想成立。最后推导了赝熵、相对赝熵与谱复杂性的精确关联，该关联可能与全息术存在联系。
英文摘要
In this work, we study pseudo entropy and spectral dynamics in quantum spin chains (Heisenberg XXZ model and the mixed-field Ising model) to investigate whether they can serve as diagnostics of quantum chaos. First, we derive an exact relation between the real part of the thermal pseudo entropy and the spectral form factor. This provided evidence that pseudo entropy could exhibit the characteristic dip, logarithmic ramp, and plateau, implying the precise manner in which pseudo entropy probes chaos. We found that the imaginary part, while it does not diagnose chaos, can still provide crucial information about Fisher zeros that is not available in the real counterpart. For spatial pseudo entropy in the XXZ chain, we find that the logarithmic critical scaling persists in both integrable and chaotic regimes, and that the non-positivity conjecture holds. Finally, we derive an exact connection between pseudo entropy, relative pseudo entropy, and spectral complexity with a potential connection to holography.
Comments15 pages, 6 figures
