The Hubbard model: bosonic excitations and zero-frequency constants

Abstract

A fully self-consistent calculation of the bosonic dynamics of the Hubbard model is developed within the composite operator method. From one side we consider a basic set of fermionic composite operators (Hubbard fields) and calculate the retarded propagators. On the other side we consider a basic set of bosonic composite operators (charge, spin and pair) and calculate the causal propagators. The equations for the Green's functions (GF) (retarded and causal), studied in the polar approximation, are coupled and depend on a set of parameters not determined by the dynamics. First, the pair sector is self-consistently solved together with the fermionic one and the zero-frequency constants (ZFC) are calculated not assuming the ergodic value, but fixing the representation of the GF in such a way to maintain the constraints required by the algebra of the composite fields. Then, the scheme to compute the charge and spin sectors, ZFCs included, is given in terms of the fermionic and pair correlators.