We use the recently developed finite cluster typical medium approach to study the Anderson localization transition in three dimensions. Applying our method to the box and binary alloy disorder distributions, we find a fast convergence with the cluster size. We demonstrate the importance of the typical medium environment and the non-local spatial correlations for the proper characterization of the localization transition. As the cluster size increases, our typical medium cluster method recovers the correct critical disorder strength for the transition. Our findings highlight the importance of the non-local cluster corrections for capturing the localization behavior of the mobility edge trajectories. Our results demonstrate that the typical medium cluster approach developed here provides a consistent and systematic description of the Anderson localization transition in the framework of the effective medium embedding schemes.

我们使用最近开发的有限簇典型介质方法来研究三个维度的安德森本地化转变。将我们的方法应用于盒形和二元合金无序分布，我们发现簇大小快速收敛。我们证明了典型的媒介环境和非本地空间相关性对本地化过渡的正确表征的重要性。随着簇大小的增加，我们典型的中等簇方法会为过渡过程恢复正确的临界无序强度。我们的发现突出了非局部聚类校正对于捕获移动性边缘轨迹的定位行为的重要性。