Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

We develop a real space cluster extension of the typical medium theory (cluster-TMT) to study Anderson localization. By construction, the cluster-TMT approach is formally equivalent to the real space cluster extension of the dynamical mean field theory. Applying the developed method to the 3D Anderson model with a box disorder distribution, we demonstrate that cluster-TMT successfully captures the localization phenomena in all disorder regimes. As a function of the cluster size, our method obtains the correct critical disorder strength for the Anderson localization in 3D, and systematically recovers the re-entrance behavior of the mobility edge. From a general perspective, our developed methodology offers the potential to study Anderson localization at surfaces within quantum embedding theory. This opens the door to studying the interplay between topology and Anderson localization from first principles.

Automated summary

A real space cluster extension method was developed to study Anderson localization, successfully capturing the phenomena in all disorder regimes. The approach accurately obtained the critical disorder strength for 3D Anderson localization and systematically recovered the re-entrance behavior of the mobility edge. This methodology offers potential to study Anderson localization at surfaces within quantum embedding theory, allowing for the exploration of the interplay between topology and Anderson localization from first principles.