Real Space and Momentum Space Cluster Methods for Strongly Disordered Systems*

The Anderson localization (AL) of electrons in disordered media continues to receive increasing interest due to the strong impact of the disorder on quantum materials. However, despite extensive studies, numerical simulations of the influence of strong disorder remains challenging. We have recently developed two kinds of cluster embedding methods to study strong disorder effects. This includes the real space cluster extension of the typical medium theory (cluster-TMT) [1] and the momentum-space cluster DCA (TM-DCA) to study Anderson localization [2]. Applying the developed methods to the Anderson tight-binding model with different types of disorder distributions, we demonstrate that both cluster methods successfully capture the localization phenomena in all disorder regimes as cluster size increases. However, we have found different accuracy and cluster size convergence of developed embedding frameworks. From a general perspective, our developed methodology offers the potential to study Anderson localization in real materials within quantum embedding theories.