Related papers: Metallic ferromagnetism in the Hubbard model: A ri…
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 $d\ge2$. We take the limits in which the Coulomb interaction and…
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…
We present the first rigorous examples of non-singular Hubbard models which exhibit ferromagnetism at zero temperature. The models are defined in arbitrary dimensions, and are characterized by finite-ranged hoppings, dispersive bands, and…
We study tight-binding models of itinerant electrons in two different bands, with effective on-site interactions expressing Coulomb repulsion and Hund's rule. We prove that, for sufficiently large on-site exchange anisotropy, all ground…
A Hubbard model with a single, partially flat band has ferromagnetic ground states. It is shown that local stability of ferromagnetism implies its global stability in such a model: The model has only ferromagnetic ground states if there are…
Thirty years ago the Hubbard model was introduced by Gutzwiller, Hubbard and Kanamori with the main purpose of mimicking the ferromagnetism of transition metals. Soon after, Nagaoka and Thouless pointed out a basic mechanism for…
We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice,…
We consider the standard repulsive Hubbard model with a flat lowest-energy band for two one-dimensional lattices (diamond chain and ladder) as well as for a two-dimensional lattice (bilayer) at half filling of the flat band. The considered…
We prove, as recently conjectured, that the ground state of the Hubbard Hamiltonian with an infinite-range hopping, when the number of electrons $N_e=N+1$ ($N$ being the number of sites), is ferromagnetic fully polarized.
We present rigorous results for the SU($n$) Fermi-Hubbard models with finite-range hopping in $d$ ($\ge 2$) dimensions. The models are defined on a class of decorated lattices. We first study the models with flat bands at the bottom of the…
We study the strong coupling limit of a two-band Hubbard Hamiltonian that also includes an inter-orbital on-site repulsive interaction $U_{ab}$. When the two bands have opposite parity and are quarter filled, we prove that the ground state…
It is well known that the Hubbard model on a line graph has a flat band and ferromagnetic ground states in a certain density range. We show that for a Hubbard model on a line graph of a planar bipartite graph the ferromagnetic ground state…
We propose a concrete model which exhibits ferromagnetism and electron-pair condensation simultaneously. The model is defined on two chains and consists of the electron hopping term, the on-site Coulomb repulsion, and a ferromagnetic…
Metallic ferromagnetism is in general an intermediate to strong coupling phenomenon. Since there do not exist systematic analytic methods to investigate such types of problems, the microscopic origin of metallic ferromagnetism is still not…
Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have…
We model conducting pentagon chains with a multi orbital Hubbard model and prove that well below half filling exact ferromagnetic ground states appear. The rigorous method we use is based on the transformation of original hamiltonian into…
Whether spin-independent Coulomb interaction in an electron system can be the origin of ferromagnetism has been an open problem for a long time. Recently, a "constructive" approach to this problem has been developed, and the existence of…
Since its introduction in 1963, the Hubbard model has becomes one of the most popular models used in the literature to study cooperative phenomena in narrow-band metals (ferromagnetism, metal-insulator transitions, charge-density waves,…
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,…
The Hubbard model is a "highly oversimplified model" for electrons in a solid which interact with each other through extremely short ranged repulsive (Coulomb) interaction. The Hamiltonian of the Hubbard model consists of two pieces; H_hop…