Ferromagnetism in the Hubbard model with a gapless nearly-flat band

Abstract

We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice, and electron hopping is assumed to be only between nearest and next nearest neighbor sites. The lattice, where all the sites are identical, is simple, and the corresponding single-electron band structure, where two cosine-type bands touch without an energy gap, is also simple. We prove that the ground state of the model is unique and ferromagnetic at half-filling of the lower band, if the lower band is nearly flat and the strength of on-site repulsion is larger than a certain value which is independent of the lattice size. This is the first example of ferromagnetism in three dimensional non-singular models with a gapless band structure.

arXiv comment25 pages, 4 figures. Ver.2: minor revision, abstract changed, figures added, typos corrected

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Cited by in corpus (3)

• Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly flat bands
• An extension of the cell-construction method for the flat-band ferromagnetism
• Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models