Cumulant approach to dynamical correlation functions

Abstract

A new theoretical approach, based on the introduction of cumulants, to calculate time dependent correlation functions at zero temperature is presented. In contrast to usual diagrammatic treatments of Green functions, the present method can be applied to operators which do not satisfy standard fermion or boson commutation relations. The introduction of cumulants is equivalent to applying the linked-cluster theorem. Thus, only ‘connected” expectation values have to be evaluated, even in cases for which Wick's theorem does not apply. The method expresses correlation functions in a form accessible to projection technique approaches. However, it circumvents a conceptual difficulty inherent in standard projection technique. There static expectation values, which are defined within the exact ground state, have to be evaluated independently. Our technique is a generalization, to dynamical aspects, of a recently introduced cumulant approach, which was restricted to the calculation of static ground-state properties. It seems to be an appropriate theoretical tool to treat the influence of strong electronic correlations like, e.g., in the new high-T _c superconducting materials. Two applications of the formalism have been given recently.