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We develop a real space cluster extension of the typical medium theory(cluster-TMT) to study Anderson localization. By construction, the cluster-TMTapproach is formally equivalent to the real space cluster extension of thedynamical mean field theory. Applying the developed method to the 3D Andersonmodel with a box disorder distribution, we demonstrate that cluster-TMTsuccessfully captures the localization phenomena in all disorder regimes. As afunction of the cluster size, our method obtains the correct critical disorderstrength for the Anderson localization in 3D, and systematically recovers there-entrance behavior of the mobility edge. From a general perspective, ourdeveloped methodology offers the potential to study Anderson localization atsurfaces within quantum embedding theory.

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