Abstract
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.
Highlights
We develop a real space quantum cluster theory based on the typical medium theory for random disorder systems
We construct the real space variant of the cluster-typical medium theory (TMT). This method by construction is similar to the cellular dynamical mean field theory [72], which is a popular cluster method effectively used for strongly interacting electron systems
Applying our real-space cluster-TMT approach to the 3D Anderson model with a box distribution, we demonstrate that the cluster-TMT is a successful self-consistent numerical approach to capture the Anderson localization transition
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Single site effective medium methods, such as the coherent potential approximation (CPA) [28,29,30,31,32,33,34,35] and the typical medium theory (TMT) [36], proved to be simple and transparent theories that are able to capture important features of the disorder effects in electron systems Common to these two methods is the mapping of the lattice problem into the impurity placed in a self-consistently determined effective medium. The developed real space cluster extension method incorporates the spatial non-local effects systemically; the re-entrance behavior of the 3D Anderson model is recovered. Unlike the single site TMT, the present real-space cluster computation captures the re-entrance behavior driven by non-local multiple scattering effects which are missing in local approximations [5,36,48,74]. The capability of describing the re-entrance can serve as a good test for our real space cluster-TMT
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
