Review: Systematic quantum cluster typical medium method for the study of localization in strongly disordered electronic systems

作     者：Terletska, Hanna Zhang, Yi Tam, Ka Ming Berlijn, Tom Chioncel, L. Vidhyadhiraja, N.S. Jarrell, Mark 

作者机构：Department of Physics and Astronomy Middle Tennessee State University Computational Science Program MurfreesboroTN37132 United States Department of Physics and Astronomy Louisiana State University Baton RougeLA70803 United States Center for Computation and Technology Louisiana State University Baton RougeLA70803 United States Center for Nanophase Materials Sciences Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Augsburg Center for Innovative Technologies University of Augsburg AugsburgD-86135 Germany Theoretical Physics Iii Center for Electronic Correlations and Magnetism University of Augsburg AugsburgD-86135 Germany Theoretical Sciences Unit Jawaharlal Nehru Center for Advanced Scientic Research Bengaluru560064 India 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2018年

核心收录：

主　　题：Electrons 

摘      要：Great progress has been made in the last several years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean field theory and the coherent potential approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization, and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium based methods mentioned above, typical medium based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states but it can also incorporate the full complexity of DFT-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medi