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

TL;DR

This paper investigates a Hubbard model on a chain of squares representing an atomic quantum wire, demonstrating flat-band ferromagnetism under specific conditions and analyzing its robustness and critical interaction strength.

Contribution

It shows that flat-band ferromagnetism can occur in a non-frustrated lattice model of an atomic quantum wire, with detailed analysis of the effects of band flatness and interaction strength.

Findings

Flat-band ferromagnetism is realized at appropriate band filling.

Ferromagnetism diminishes as Hubbard U increases due to the band not being at the bottom.

Critical U value for ferromagnetism is within realistic parameters.

Abstract

We have examined a Hubbard model on a chain of squares, which was 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 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.