The charge and spin sectors of the $t$-$t'$ Hubbard model

TL;DR

This paper presents a self-consistent calculation of the charge and spin sectors in the $t$-$t'$ Hubbard model using a two-pole approximation, extending previous methods to better understand cuprate properties.

Contribution

It introduces an extended approximation scheme for the bosonic sectors of the Hubbard model, improving the description of charge and spin dynamics in correlated materials.

Findings

Effective description of charge and spin excitations in the $t$-$t'$ Hubbard model.

Extension of previous fermionic and bosonic sector calculations.

Potential insights into the magnetic response of cuprates.

Abstract

The charge and spin sectors, which are intimately coupled to the fermionic one, of the $t$-$t'$ Hubbard model have been computed self-consistently within the two-pole approximation. The relevant unknown correlators appearing in the causal bosonic propagators have been computed by enforcing the constraints dictated by the hydrodynamics and the algebra of the composite operators coming into play. The proposed scheme of approximation extends previous calculations made for the fermionic sector of the $t$-$t'$ Hubbard model and the bosonic sector of the Hubbard model, which showed to be very effective to describe the overdoped region of cuprates (the former) and the magnetic response of their parent compounds (the latter).