Abstract
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.
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