Bosonic sector of the two-dimensional Hubbard model studied within a two-pole approximation

TL;DR

This paper investigates the charge and spin dynamics of the two-dimensional Hubbard model using a two-pole approximation, achieving results consistent with numerical methods and providing insights into the model's response functions.

Contribution

It introduces a fully self-consistent two-pole approximation approach within the Composite Operator Method for the Hubbard model's bosonic sector, without decoupling.

Findings

Results agree with existing numerical calculations

Detailed temperature and momentum dependencies obtained

Response functions show rich momentum dependence

Abstract

The charge and spin dynamics of the two-dimensional Hubbard model in the paramagnetic phase is first studied by means of the two-pole approximation within the framework of the Composite Operator Method. The fully self-consistent scheme requires: no decoupling, the fulfillment of both Pauli principle and hydrodynamics constraints, the simultaneous solution of fermionic and bosonic sectors and a very rich momentum dependence of the response functions. The temperature and momentum dependencies, as well as the dependency on the Coulomb repulsion strength and the filling, of the calculated charge and spin susceptibilities and correlation functions are in very good agreement with the numerical calculations present in the literature.