The local quantum cluster typical medium approach for disordered systems.

Due to the non-self-averaging nature of strong disorder Anderson localized states, the effective medium theories based on the linear (algebraic) averaging over disorder, often fail to capture the localized states. Recently, it has been shown that the typical medium treatment that utilizes the geometric averaging over disorder can successfully detect the disorder localized states. Constructing a proper numerical ansatz that can capture the localized states is often a challenge, especially for more complex systems with the disorder. We have recently revised our quantum cluster typical medium approach (TM-DCA) and constructed a simplified local quantum cluster ansatz for the typical density of states. We performed a careful systematic analysis of the new local quantum cluster ansatz for both the box and binary disorder distributions in the three-dimensional Anderson model. Our results show that, close to the Anderson transition, the local effects are dominant. We found that the new approach allows us to properly capture the critical value of disorder for the phase transition in a less expensive computational way, however, the convergence of the mobility edges is slow with respect to the cluster size.