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.
@article{arxiv.2109.14267,
title = {Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization},
author = {Ka-Ming Tam and Hanna Terletska and Tom Berlijn and Liviu Chioncel and Juana Moreno},
journal= {arXiv preprint arXiv:2109.14267},
year = {2021}
}