Quantum cluster theories for disordered electron systems.

Recently, quantum cluster theories have been developed to understand the properties of disordered electronic systems. The disorder is a common and often unavoidable feature of many materials. It plays a critical role in determining and controlling the properties of many functional quantum systems. Anderson localization is one of such fascinating effects of disorder and is often challenging to capture numerically. In this talk, I will discuss the recently developed Typical Medium Dynamical Cluster Approximation (TMDCA) [1], an effective medium quantum cluster approach for disordered systems. The TMDCA enables quantitative analysis of electron localized states in disordered electron systems. Following the ideas of Dobrosavljevic et al. [2], the TMDCA employs the cluster typical (geometrically averaged) density of states as an order parameter to detect the localized electrons states. It has been shown that TMDCA not only correctly captures non-local effects but also recovers exact analytical results in simple disorder models [1]. I will also provide an overview of various recent applications of the TMDCA to a variety of models and systems, including the application of the method to interacting disordered electrons as well as realistic systems in the framework of the ab-initio methods.
[1] Hanna Terletska, Yi Zhang, Ka Ming Tam, Tom Berlijn, Liviu Chioncel, N.S. Vidhyadhiraja, Mark Jarrell, Review: App. Sci. 8, 12 (2018).
[2] V. Dobrosavljevic, A. A. Pastor, B. K. Nikolic, Europhys. Lett. 62, 76 (2003).