Ferromagnetism in a Hubbard model for an atomic quantum wire: A realization of flat-band magnetism from even-membered rings

We have examined as a Hubbard model on a chain of squares, which was as proposed by Yajima et al. as a model of an atomic quantum wire As/Si(100), to show that the flat-band ferromagnetism according to a kind of Mielke-Tasaki mechanism should be realized for an appropriate band filling in such a nonfrustrated lattice. Reflecting the fact that the flat band is not a bottom one, the ferromagnetism vanishes, rather than intensifies, as the Hubbard $U$ is increased. The exact-diagonalization method is used to show that the critical value of $U$ is in a realistic range. We also discussed the robustness of the magnetism against the degradation of the flatness of the band.