Dynamical Mean Field Theory

Abstract

In the ordinary mean field theory, the effective field is static. If one allows temporal variation of the effective field, fluctuation effects of the corresponding field can be included. The correlation problem in a large system is then replaced by a single-site problem surrounded by a dynamical effective medium. The effective impurity system is regarded as zero-dimensional. It can be shown that the replacement by an effective impurity is exact in the limit of large number of neighboring sites, which is the case in infinite dimensions. Hence the zero and infinite dimensions are connected continuously. In this way the dynamical mean field theory (DMFT) approaches actual three-dimensional systems from the infinite-dimensional limit. The DMFT has achieved remarkable success in understanding those many-body effects which come from strong local correlations. This chapter explains the DMFT starting with the background of its development.