Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
1997-12-18
Physics
Condensed Matter
Strongly Correlated Electrons
LaTeX2e, 72 pages, 17 epsf figures. Many minor corrections made in March 1998. This is the final version, which will appear in
Scientific paper
10.1143/PTP.99.489
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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