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

Abstract

We have modeled an atomic quantum wire As/Si(100) as a Hubbard model on a chain of squares as proposed by Yajima et al to show that the flat-band ferromagnetism according to the Mielke-Tasaki theorem should be realized for an appropriate band filling. This provides a unique manifestation of the theorem in a non-frustrated lattice. Reflecting the fact that the flat band is not a bottom one, the ferromagnetism vanishes, rather than intensified, 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.