  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.
