发表机构
Motilal Nehru National Institute of Technology Allahabad（莫蒂拉尔·尼赫鲁国家技术学院安拉阿巴德分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究非均匀XXZ自旋链中OTOCs与ETH的联系，利用确定性空间变化相互作用分布，发现有限相互作用梯度引发信息扰乱不对称，通过两种互补方法阐明其不对称有限尺寸长时间饱和值起源，解析预测与数值结果一致。
AI 中文摘要
在实验设计的量子多体系统中，确定性空间不均匀性愈发重要，相互作用梯度会强烈影响非平衡动力学。受此启发，我们研究了非均匀XXZ自旋链中的乱序关联函数（OTOCs）及其与本征态热化假设（ETH）的联系。利用确定性空间变化的相互作用分布，我们表明有限的相互作用梯度（δ>0）会在信息扰乱中引发明显的左右不对称，由OTOCs量化。即使系统呈现量子混沌的谱特征，这种不对称依然存在，强相互作用侧的算符表现出受抑制的扰乱。为阐明OTOCs不对称有限尺寸长时间饱和值的起源，我们采用了两种互补方法。首先，在ETH框架内分析能量本征基中OTOC可观测量的对角矩阵元。其次，基于哈密顿量与OTOC可观测量之间的重叠推导出有限尺寸饱和值的解析表达式，该表达式明确纳入了空间相互作用分布。解析预测与数值结果完全一致，并为确定性相互作用梯度如何在OTOCs的长时间饱和中产生观察到的不对称提供了微观解释。
英文摘要
Inhomogeneous systems have become increasingly relevant in experimentally engineered quantum many-body systems, where spatially varying interaction strengths can significantly influence nonequilibrium dynamics. Motivated by this, we numerically study the out-of-time-ordered correlators (OTOCs) in inhomogeneous XXZ spin chains. Using two types of spatially varying interaction profiles, namely, linear-gradient and stepwise profiles, we show that spatial inhomogeneity in the interactions can induce pronounced asymmetry in information scrambling, with OTOC operators located at different sites exhibiting distinct dynamical behavior. In particular, OTOCs associated with the strongly interacting side exhibit suppressed scrambling compared to those associated with the weakly interacting side, with the difference becoming more pronounced when the interaction strengths differ significantly. To elucidate the origin of the long-time saturation of OTOCs, we analyze the diagonal matrix elements of the OTOC observables in the energy eigenbasis and their overlap with the Hamiltonian, which explicitly incorporates the spatial interaction profile. The resulting analytical expression is consistent with the numerical results. Finally, we extend our analysis to periodically driven inhomogeneous spin chains and show that the interaction-gradient-induced asymmetry persists under periodic driving.
Comments13 pages,11 figures
