Existence of Saturated Ferromagnetic and Spiral States in 1D Lieb-Ferrimagnetic Models away from Half-Filling

Abstract

In order to study conditions for the appearance of ferromagnetism in a wide filling region, we investigate numerically three types of one-dimensional Lieb-ferrimagnetic Hubbard models: a periodic diamond (PD) chain, a periodic alternately-attached leg (PAAL) chain and an open diamond (OD) chain. All of these models have a flat band (or equivalently, degenerate single-electron eigenvalues). The PD and OD chains commonly have a local-loop structure. Nagaoka's theorem holds only in the PD chain. At half-filling, it have been rigorously proven that all of these models are ferrimagnet. Away from half-filling, however, quite different magnetic properties are found. In the fillings 1/3< rho_e <1/2, the ground state of the PD chain for a infinitely-large U is the extended ferromagnetic state, that is, the saturated ferromagnetic state or the spiral state for odd or even number of electrons, respectively. In the PAAL chain, on the other hand, there is no magnetic order. Thus, the flat band is found to be not a sufficient condition of the extended ferromagnetic state. We find, moreover, that the saturated ferromagnetism appears in the OD chain, although the Nagaoka theorem does not hold on this chain. This indicates that the local-loop structure plays an important role on the appearance of the extended ferromagnetic state.

4 pages, 4 figures, 2 tables. to be published in J. Phys. Soc. Jpn. Vol. 68 No. 9

References in corpus (4)

• From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
• Ferromagnetism in a Hubbard model for an atomic quantum wire: a realization of flat-band magnetism from even-membered rings
• Aspects of the ground state of the $U=\infty$ Hubbard ladder
• Spectral function of the spiral spin state in the trestle and ladder Hubbard model

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• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph