4,374 research outputs found
Ferromagnetism in the Hubbard model: A constructive approach
It is believed that strong ferromagnetic orders in some solids are generated
by subtle interplay between quantum many-body effects and spin-independent
Coulomb interactions between electrons. Here we describe our rigorous and
constructive approach to ferromagnetism in the Hubbard model, which is a
standard idealized model for strongly interacting electrons in a solid. We
introduce a class of Hubbard models in any dimensions which are nonsingular in
the sense that both the Coulomb interaction and the density of states (at the
Fermi level) are finite. We then prove that the ground states of the models
exhibit saturated ferromagnetism, i.e., have maximum total spins. Combined with
our earlier results, the present work provides nonsingular models of itinerant
electrons with only spin-independent interactions where low energy behaviors
are proved to be that of a ``healthy'' ferromagnetic insulator.Comment: 34 pages (References have been added in v2. Many small changes have
been made in v3. Minor typos fixed in v4.
From Nagaoka's ferromagnetism to flat-band ferromagnetism and beyond: An introduction to ferromagnetism in the Hubbard model
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.Comment: 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
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