The Hubbard model: bosonic excitations and zero-frequency constants

TL;DR

This paper develops a self-consistent method to analyze bosonic excitations in the Hubbard model, calculating Green's functions and zero-frequency constants while maintaining algebraic constraints, advancing understanding of correlated electron systems.

Contribution

It introduces a comprehensive self-consistent approach within the Composite Operator Method to compute bosonic dynamics and zero-frequency constants in the Hubbard model.

Findings

Calculated retarded and causal Green's functions for charge, spin, and pair sectors.

Determined zero-frequency constants without assuming ergodicity.

Maintained algebraic constraints to ensure physical consistency.

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 constrains 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.