论文标题
探测千古态的随机性：厄运和多体积定位的极值统计数据
Probing the randomness of ergodic states: extreme-value statistics in the ergodic and many-body-localized phases
论文作者
论文摘要
检查了具有多体定位过渡的无序旋转链中纠缠频谱的极端价值统计。可以预期，金属或厄尔及性相中的特征状态以随机状态为例，因此，通常称为纠缠频谱的还原密度矩阵的特征值将遵循痕量标准化的WishArt Enesemble的特征值统计量。特别是，特征值的密度应该遵循普遍的Marchenko-Pastur分布。我们发现，尾巴的偏差均与无序XXZ的偏差，在半填充扇区中保存了总$ S_Z $，以及打破这种保护的模型。最大的特征值提供了对偏差的敏感度量，在适当移动和缩放后的Wishart合奏中，该值遵循了通用的Tracy-Widom分布。我们表明，对于在金属阶段考虑的模型，特征向量降低的密度矩阵的最大特征值遵循了与Fisher-Tipett-Gumbel分布接触的广义极值统计，这表明与Dishart Ensemble相比，特征值之间的相关性较弱。我们通过分布在高熵和归一化参与率的条件下显示，条件纠缠频谱仍然遵循广义的极值分布。在深度的局部阶段，我们发现了最大和第二大特征值的适当缩放功能的重型尾部分布和Lévy稳定法律。缩放是由最近开发的弱耦合混沌系统的扰动理论激发的。
The extreme-value statistics of the entanglement spectrum in disordered spin chains possessing a many-body localization transition is examined. It is expected that eigenstates in the metallic or ergodic phase, behave as random states and hence the eigenvalues of the reduced density matrix, commonly referred to as the entanglement spectrum, are expected to follow the eigenvalue statistics of a trace normalized Wishart ensemble. In particular, the density of eigenvalues is supposed to follow the universal Marchenko-Pastur distribution. We find deviations in the tails both for the disordered XXZ with total $S_z$ conserved in the half-filled sector as well as in a model that breaks this conservation. A sensitive measure of deviations is provided by the largest eigenvalue, which in the case of the Wishart ensemble after appropriate shift and scaling follows the universal Tracy-Widom distribution. We show that for the models considered, in the metallic phase, the largest eigenvalue of the reduced density matrix of eigenvector, instead follows the generalized extreme-value statistics bordering on the Fisher-Tipett-Gumbel distribution indicating that the correlations between eigenvalues are much weaker compared to the Wishart ensemble. We show by means of distributions conditional on the high entropy and normalized participation ratio of eigenstates that the conditional entanglement spectrum still follows generalized extreme value distribution. In the deeply localized phase we find heavy tailed distributions and Lévy stable laws in an appropriately scaled function of the largest and second largest eigenvalues. The scaling is motivated by a recently developed perturbation theory of weakly coupled chaotic systems.
