Conclusion

Abstract

Two decades have passed since first ideas appeared leading to development of Dynamical Mean-Field Theory (DMFT) that becomes now a basic method to study strongly correlated systems (SCS). During this time hundreds of theoretical works were done using DMFT to study as basic models as well as real materials where physics is determined by correlation effects. A basic approximation of DMFT is neglect of spatial correlations with full description of local dynamical fluctuations. That is equivalent to approximation where self-energy is local depending only on frequency but not on wave vector. In DMFT method lattice problem is mapped on single-site impurity problem where atom with Coulomb interaction among electrons in d or f shell is embedded in energy (or time) dependent Weiss field (hence the name of the method: dynamical mean field). Spatial correlations neglect is justified when the system is not close to transition in long-range ordering state so that long coherent length fluctuations do not develops. With very few exceptions like high-T _c cuprates such conditions are realized in real materials and DMFT method was very successful in vast majority of applications.