Metallic ferromagnetism supported by a single band in a multi-band Hubbard model

Abstract

We construct a multi-band Hubbard model on the lattice obtained by "decorating" a closely packed $d$-dimensional lattice $\mathcal{M}$ (such as the triangular lattice) where $d\ge 2$. We take the limits in which the Coulomb interaction and the band gap become infinitely large. Then there remains only a single band with finite energy, on which electrons are supported. Let the electron number be $N_{\mathrm{e}}=|\mathcal{M}|-N_{\mathrm{h}}$, where $|\mathcal{M}|$ corresponds to the electron number which makes the lowest (finite energy) band half-filled, and $N_{\mathrm{h}}$ is the number of "holes". It is expected that the model exhibits metallic ferromagnetism if $N_{\mathrm{h}}/|\mathcal{M}|$ is nonvanishing but sufficiently small. We prove that the ground states exhibit saturated ferromagnetism if $N_{\mathrm{h}}\le (\text{const.})|\mathcal{M}{|}^{2/(d+2)}$, and exhibit (not necessarily saturated) ferromagnetism if $N_{\mathrm{h}}\le (const.)|\mathcal{M}{|}^{(d+1)/(d+2)}$. This may be regarded as a rigorous example of metallic ferromagnetism provided that the system size $|\mathcal{M}|$ is not too large.

23 pages, 9 figures. version 2: some changes, 3 references added, typos corrected

References in corpus (2)

• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• Exact Results on Itinerant Ferromagnetism in Multi-orbital Systems on Square and Cubic Lattices

Cited by in corpus (2)

• An extension of the cell-construction method for the flat-band ferromagnetism
• Ferromagnetism in the Hubbard model with a gapless nearly-flat band