发表机构
School of Physics and Astronomy, University of Nottingham; Taishan College, Shandong University; Centre for the Mathematics and Theoretical Physics of Quantum Non-equilibrium Systems, University of Nottingham; School of Physics, Henan Normal University（诺丁汉大学物理与天文学学院; 山东大学泰山学堂; 诺丁汉大学量子非平衡系统数学与理论物理中心; 河南师范大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过精确对角化和Lanczos递归，发现倾斜扩展玻色-哈伯德链在U≈V时Krylov复杂度饱和呈尖锐脊状而谱统计仍部分混沌，表明Krylov复杂度能提供谱诊断无法捕捉的多体混沌信息。
AI 中文摘要
我们研究了同时存在在位相互作用$U$和最近邻相互作用$V$的倾斜扩展玻色-哈伯德链中的Krylov态复杂度。该倾斜扩展玻色-哈伯德模型可通过光晶格中的里德伯修饰相互作用实现。利用精确对角化和Lanczos递归，从三个物理动机明确的Fock态出发，我们计算了开放链在单位填充下的含时复杂度、其长时间饱和值以及Lanczos系数的涨落。关键的是，我们在$U\simeq V$附近识别出一个显著的准混沌对角区，在该区域中Krylov复杂度饱和呈现尖锐脊状结构，而谱能级间距统计仍保持部分混沌。这种分离源于在位与最近邻相互作用的竞争，它生成了密集的近共振多体构型流形，该流形被态依赖动力学高效耦合，但保留了残余的谱结构。我们的结果表明，Krylov态复杂度提供了关于多体混沌的互补的、态敏感的信息，这些信息无法仅通过谱诊断获得，从而确立了Krylov复杂度作为研究实验可及量子模拟器中热化和信息扰乱的有用诊断工具。
英文摘要
We investigate Krylov state complexity in a tilted extended Bose-Hubbard chain in which both the on-site interaction $U$ and nearest-neighbor interaction $V$ are present. The tilted extended Bose-Hubbard model can be realized with Rydberg-dressed interactions in optical lattices. Using exact diagonalization and Lanczos recursion from three physically motivated Fock states, we compute the time-dependent complexity, its long-time saturation value, and the fluctuations of the Lanczos coefficients for an open chain at unit filling. Crucially, we identify a pronounced quasi-chaotic diagonal regime near $U\simeq V$ in which the Krylov complexity saturation exhibits a sharp ridge while the spectral level-spacing statistics remain partially chaotic. This dissociation arises from the competition between the on-site and nearest-neighbor interaction, which generates a dense manifold of near-resonant many-body configurations that is efficiently coupled by the state-dependent dynamics but retains residual spectral structure. Our results show that Krylov state complexity provides complementary, state-sensitive information about many-body chaos that is not captured by the spectral diagnostics alone, establishing Krylov complexity as a useful diagnostic for studying thermalization and information scrambling in experimentally accessible quantum simulators.
Comments10 pages, 5 figures
