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 proves that Nagaoka's ferromagnetism is stable under the influence of the qunantized radiation field.
Some rigorous results on the Holstein-Hubbard model
Electron-phonon interaction in Kondo lattice systems
Ground state properties of the Holstein-Hubbard model
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