Strong electronic correlations: Dynamical mean-field theory and beyond

Abstract

This chapter aims at a pedagogical introduction to theoretical approaches of strongly correlated materials based on dynamical mean-field theory (DMFT) and its extensions. The goal of this theoretical construction is to retain the many-body aspects of local atomic physics within the extended solid. After introducing the main concept at the level of the Hubbard model, we briefly review the theoretical insights into the Mott metal-insulator transition that DMFT provides. We then describe realistic extensions of this approach which combine the accuracy of first-principle Density-Functional Theory with the treatment of local many-body effects within DMFT. We further provide an elementary discussion of the continuous-time Quantum Monte Carlo schemes for the numerical solution of the DMFT effective quantum impurity problem. Finally, the effects of short-range non-local correlations within cluster extensions of the DMFT scheme, as well as long-range fluctuations within the fully renormalized dual-fermion perturbation scheme are discussed extensively. © 2012 Springer-Verlag Berlin Heidelberg.