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

TL;DR

This paper introduces a real space cluster extension of the typical medium theory to effectively model Anderson localization in three-dimensional disordered systems, capturing critical phenomena and re-entrance behavior.

Contribution

The authors develop a cluster-TMT method that is equivalent to real space cluster DMFT, enabling accurate analysis of Anderson localization across all disorder regimes.

Findings

Successfully captures localization phenomena in 3D

Accurately predicts critical disorder strength

Recovers re-entrance behavior of mobility edge

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.