Quantum Cluster Embedding DMFT Description of Electron Localization in Disordered and Strongly Correlated Systems*

Dynamical Mean Field Theory (DMFT) and its quantum cluster embedding schemes—DCA (Dynamical Cluster Approximation), CDMFT (Cluster DMFT), and TMDCA (Typical Medium DCA)—serve as robust computational tools to address the critical non-local spatial correlations posed by interaction and disorder-induced phase transitions. In this study, we use these cluster embedding DMFT methods to both two and three-dimensional Anderson and Hubbard models. Our findings underscore pronounced non-local, long-range correlation effects around localizations, emphasizing the important role of non-local descriptions in capturing metal-insulator transitions in such systems. Furthermore, we conduct a comparative benchmark between various quantum cluster embedding DMFT techniques, accentuating their precision in delineating metal-to-insulator phase transitions within the Hubbard and Anderson model frameworks.