Influence of Spin Wave Excitations on the Ferromagnetic Phase Diagram in the Hubbard-Model

TL;DR

This paper advances the theoretical understanding of spin wave excitations in the Hubbard model by extending the RPA with a spectral-density approach, revealing a reduced ferromagnetic phase compared to standard theories.

Contribution

It introduces a spectral-density-ansatz extension to RPA for the Hubbard model, incorporating a screened Coulomb interaction to improve physical accuracy of spin wave dispersions.

Findings

Reduced ferromagnetic phase in phase diagrams

Improved spin wave dispersion calculations

Enhanced theoretical framework for collective excitations

Abstract

The subject of the present paper is the theoretical description of collective electronic excitations, i.e. spin waves, in the Hubbard-model. Starting with the widely used Random-Phase-Approximation, which combines Hartree-Fock theory with the summation of the two-particle ladder, we extend the theory to a more sophisticated single particle approximation, namely the Spectral-Density-Ansatz. Doing so we have to introduce a `screened` Coulomb-interaction rather than the bare Hubbard-interaction in order to obtain physically reasonable spinwave dispersions. The discussion following the technical procedure shows that comparison of standard RPA with our new approximation reduces the occurrence of a ferromagnetic phase further with respect to the phase-diagrams delivered by the single particle theories.