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      From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model

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          Abstract

          This is a self-contained review about ferromagnetism in the Hubbard model, which should be accessible to readers with various backgrounds who are new to the field. We describe Nagaoka's ferromagnetism and flat-band ferromagnetism in detail, giving all necessary backgrounds as well as complete (but elementary) mathematical proofs. By studying an intermediate model called long-range hopping model, we also demonstrate that there is indeed a deep relation between these two seemingly different approaches to ferromagnetism. We further discuss some attempts to go beyond these approaches. We briefly discuss recent rigorous example of ferromagnetism in the Hubbard model which has neither infinitely large parameters nor completely flat bands. We give preliminary discussions about possible experimental realizations of the (nearly-)flat-band ferromagnetism. Finally we focus on some theoretical attempts to understand metallic ferromagnetism. We discuss three artificial one-dimensional models in which the existence of metallic ferromagnetism can be easily proved.

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          Most cited references 8

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          Ferromagnetism in multi--band Hubbard models: From weak to strong Coulomb repulsion

          We propose a new mechanism which can lead to ferromagnetism in Hubbard models containing triangles with different on-site energies. It is based on an effective Hamiltonian that we derive in the strong coupling limit. Considering a one-dimensional realization of the model, we show that in the quarter-filled, insulating case the ground-state is actually ferromagnetic in a very large parameter range going from Tasaki's flat-band limit to the strong coupling limit of the effective Hamiltonian. This result has been obtained using a variety of analytical and numerical techniques. Finally, the same results are shown to apply away from quarter-filling, in the metallic case.
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            Note on the Ground States of Systems with the Strong Hund-Coupling

             Kenn Kubo (1982)
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              Large Fermi surface of the one-dimensional Kondo lattice model

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                Author and article information

                Journal
                17 December 1997
                1998-03-09
                Article
                10.1143/PTP.99.489
                cond-mat/9712219
                Custom metadata
                LaTeX2e, 72 pages, 17 epsf figures. Many minor corrections made in March 1998. This is the final version, which will appear in Prog. Theor. Phys. 99 (invited paper)
                cond-mat.str-el

                Condensed matter

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