Theory of itinerant magnetism in the infinite U Hubbard model

We develop a perturbation theory in the strong coupling limit of Hubbard model in one dimension and derive effective magnetic interactions. Importantly, this theory works for any electron density away from 0. The derived magnetic interaction is ferromagnetic or antiferromagnetic depending on the signs of the hopping integrals. In the former case, this shows the robustness of Nagaoka ferromagnetism for a finite density of doped holes—we believe this to be the first demonstration of its relevance in the thermodynamic limit. We also present the magnetic phase diagram obtained from density matrix renormalization group calculations, which corroborates our conclusions. Finally, we comment on higher dimensional generalizations.