1Dynamical Mean-Field Theory

Abstract. The dynamical mean-field theory (DMFT) is a widely applicable approx-imation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particu-lar, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equa-tions, and present several applications which have provided important insights into the properties of correlated matter