Strongly Correlated Systems in Infinite Dimensions and Their Zero Dimensional Counterparts

Abstract

We extend a mapping from infinite dimensional to zero dimensional (impurity) models to derive mean field equations of several strongly correlated systems which become exact in infinite dimensions. We discuss various magnetic phases of the Hubbard model, the periodic Anderson model the Kondo lattice and the Falicov Kimball model and we relate them to different impurity models. Qualitative insights into these models is gained from the exact results obtained for their zero dimensional counterparts.