We discuss the problem of localization in two dimensional electron systems in the quantum Hall (single Landau level) regime. After briefly summarizing the well-studied problem of Anderson localization in the non-interacting case, we concentrate on the problem of disorder induced many-body localization (MBL) in the presence of electron–electron interactions using numerical exact diagonalization and eigenvalue spacing statistics as a function of system size. We provide evidence showing that MBL is not attainable in a single Landau level with short range (white noise) disorder in the thermodynamic limit. We then study the interplay of topology and localization, by contrasting the behavior of topological and nontopological subbands arising from a single Landau level in two models – (i) a pair of extremely flat Hofstadter bands with an optimally chosen periodic potential, and (ii) a Landau level with a split-off nontopological impurity band. Both models provide convincing evidence for the strong effect of topology on the feasibility of many-body localization as well as slow dynamics starting from a nonequilibrium state with charge imbalance.

我们讨论了量子霍尔（单朗道能级）体系中二维电子系统的局部化问题。在简要总结了在非交互情况下经过充分研究的安德森定位问题之后，我们使用数值精确对角化和本征值间距统计数据，着重讨论了在存在电子与电子相互作用的无序诱导多体定位（MBL）问题。系统大小的函数。我们提供的证据表明，在热力学极限内短距离（白噪声）无序的单个Landau水平上无法达到MBL。然后，我们研究拓扑和本地化的相互作用，通过在两个模型中比较由单个Landau能级引起的拓扑和非拓扑子带的行为–（i）一对具有最佳选择的周期性势的极其平坦的Hofstadter能带，以及（ii）具有分离的非拓扑杂质的Landau能级乐队。两种模型都提供了令人信服的证据，证明拓扑结构对多体定位的可行性具有强大的影响，以及从具有电荷不平衡的非平衡态开始的缓慢动力学。