Nagaoka's theorem in the Holstein-Hubbard model

TL;DR

This paper extends Nagaoka's theorem to the Holstein-Hubbard model, demonstrating the stability of ferromagnetism despite electron-phonon interactions and quantized radiation fields, thus broadening the theorem's applicability.

Contribution

It generalizes Nagaoka's theorem to include electron-phonon interactions and quantized radiation, showing the robustness of ferromagnetism in these extended models.

Findings

Nagaoka's ferromagnetism remains stable with electron-phonon interactions.

Ferromagnetism persists under quantized radiation fields.

Theoretical proof of stability in extended models.

Abstract

Nagaoka's theorem on ferromagnetism in the Hubbard model is extended to the Holstein-Hubbard model. This shows that Nagaoka's ferromagnetism is stable even if the electron-phonon interaction is taken into account. We also prove that Nagaoka's ferromagnetism is stable under the influence of the quantized radiation field.