We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.

中文翻译：

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几乎多机体本地化系统中的几乎守恒的操作员

我们构造一维保守的局部算子，该算子在系统的哈密顿量附近具有最小的换向器，且靠近一维无序自旋链的多体局部化转变。我们使用精确的对角线化和张量网络来收集这些慢速算符在不同支撑大小和无序强度下的统计信息。我们的结果表明，最小换向器的平均值随支撑尺寸的缩放对热阶段的格里菲思效应和多体定位的开始很敏感。此外，我们证明了换向器的概率分布可以使用极值理论进行分析，并且它们的尾巴揭示了热相中扩散和次扩散动力学之间的差异。