局域林德布拉德算符中的本征算子纠缠统计
Eigenoperator Entanglement Statistics in Local Lindbladians
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中文总结 AI 辅助
本研究通过Kullback-Leibler散度分析局域Lindbladians的本征算子纠缠统计，发现局域性导致偏离随机矩阵预测，并引入迭代σ-裁剪方案揭示普适的对数正态纠缠分布，该分布适用于不同对称类的耗散Ising链。
中文摘要 AI 辅助
随机矩阵谱统计被广泛用于诊断开放系统中的量子混沌，但混沌特征值关联是否伴随Haar典型的本征算子仍不清楚。我们研究了具有近最大纠缠的Liouvillian本征算子的算子纠缠统计，类似于哈密顿系统中谱中部的态。利用Kullback-Leibler散度，我们表明Haar随机统计能准确描述Ginibre和类AI$^\dagger$高斯系综。对于纯耗散随机Lindbladians，我们发现跳变算子的局域性极大地改变了本征算子纠缠统计。非局域Lindbladians保持相对接近Haar随机行为，而局域Lindbladians则随着系统尺寸的增加越来越偏离随机矩阵统计。此外，与哈密顿系统不同，局域Lindbladians的最高纠缠本征算子通常不位于态密度最大的区域，这是由于复本征谱的聚集结构所致。我们引入了一种迭代的$\sigma$-裁剪方案，无需预先选择谱窗口即可提取高纠缠分布，并发现该分布对于非局域Lindbladians是高斯分布，而对于局域Lindbladians则是对数正态分布。值得注意的是，相同的对数正态分布（无需额外拟合）也描述了属于不同非厄米对称类的耗散混合场Ising链。因此，我们的结果指出了局域Lindbladians的普适本征算子纠缠分布，而这种分布并未被一般的非厄米随机矩阵系综所捕获。
英文摘要
Random matrix spectral statistics are widely used to diagnose quantum chaos in open systems, but whether chaotic eigenvalue correlations are accompanied by Haar-typical eigenoperators remains unclear. We study the operator-entanglement statistics of Liouvillian eigenoperators with near-maximal entanglement, analogous to states near the middle of the spectrum in Hamiltonian systems. Using the Kullback-Leibler divergence, we show that Haar-random statistics accurately describe both the Ginibre and class-AI$^\dagger$ Gaussian ensembles. For purely dissipative random Lindbladians, we find that locality of the jump operators drastically alters the eigenoperator-entanglement statistics. Nonlocal Lindbladians remain relatively close to Haar-random behavior, whereas local Lindbladians deviate increasingly from random-matrix statistics with system size. Moreover, unlike in Hamiltonian systems, the most highly entangled eigenoperators of local Lindbladians do not generally lie in the region of largest density of states, owing to the clustered structure of the complex eigenspectrum. We introduce an iterative $σ$-clipping scheme to extract the high-entanglement distribution without preselecting a spectral window, and find that it is Gaussian for nonlocal Lindbladians but log-normal for local ones. Remarkably, the same log-normal distribution, with no additional fitting, also describes dissipative mixed-field Ising chains belonging to distinct non-Hermitian symmetry classes. Our results therefore point to a universal eigenoperator-entanglement distribution for local Lindbladians that is not captured by generic non-Hermitian random-matrix ensembles.
发表机构
- School of Physics, Peking University（北京大学物理学院）
- Center for High Energy Physics, Peking University（北京大学高能物理中心）
机构由 AI 辅助整理，请以论文原文为准。
