发表机构
Julius-Maximilians-Universität Würzburg; Shanghai Jiao Tong University; Pohang University of Science and Technology; Instituto de Física Teórica UAM/CSIC（维尔茨堡大学; 上海交通大学; 韩国科学技术院; 马德里自治大学/西班牙国家科学研究委员会理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出展开的Krylov复杂度方法，通过预处理能谱消除可积系统的虚假混沌峰值，实现对真实多体 scrambling 的更可靠诊断。
AI 中文摘要
诊断量子混沌的核心挑战在于区分真实的多体 scrambling 与能谱的运动学效应。Krylov态复杂度（又称扩展复杂度）已成为一种强大的诊断工具，其特征性的增长、峰值和弛豫常被视为混沌的标志。然而，此前研究表明该判据会产生假阳性结果：以鞍点为主的可积系统即使没有随机矩阵能级关联，也可能出现显著峰值。我们基于互补的数值和分析证据论证，通过在构建后续Krylov动力学前对能谱进行展开可解决这一歧义。展开操作会移除非普适的平滑态密度，同时保留微观能谱关联，从而抑制可积系统中的虚假峰值，同时保留混沌系统的普适能谱特征。分析上，用正交多项式表述的Lanczos迭代产生了具有稳健近对角结构的精确复杂度核，其精细特征反映了 underlying 的能谱关联。此外，对于对数模型，可精确执行展开操作，将能谱映射为均匀晶格，得到可消除假阳性峰值的解析扩展复杂度。这些发现确立了展开的Krylov复杂度作为更可靠的真实多体scrambling探针的地位。
英文摘要
A central challenge in diagnosing quantum chaos is to distinguish genuine many-body scrambling from kinematic effects of the spectrum. Krylov state complexity, or spread complexity, has emerged as a powerful diagnostic, with its characteristic growth, peak, and relaxation often taken as signatures of chaos. However, previous work has shown that this criterion can give false positives: saddle-dominated integrable systems may display prominent peaks even without random-matrix level correlations. We argue, based on complementary numerical and analytical evidence, that this ambiguity can be resolved by unfolding the spectrum prior to constructing the ensuing Krylov dynamics. By removing the non-universal smooth density of states while retaining microscopic spectral correlations, unfolding suppresses spurious peaks in integrable systems while preserving the universal spectral signatures of chaotic systems. Analytically, the formulation of the Lanczos iteration in terms of orthogonal polynomials yields an exact complexity kernel with a robust near-diagonal structure whose fine-grained features reflect the underlying spectral correlations. Moreover, for the logarithmic model, unfolding can be performed exactly, mapping the spectrum to a uniform lattice and yielding an analytic spread complexity that removes the false-positive peak. These findings establish unfolded Krylov complexity as a more reliable probe of genuine many-body scrambling.
Commentsv1: 15 pages, 9 figures, v2: references added, minor changes
