Flat-band ferromagnetism in the SU($N$) Hubbard and Kondo lattice models

Abstract

We develop a general theory of flat-band ferromagnetism in the SU($N$) Fermi-Hubbard model, which describes the behavior of $N$-component fermions with SU($N$) symmetric interactions. We focus on the case where the single-particle spectrum has a flat band and establish a necessary and sufficient condition for the SU($N$) Hubbard model to exhibit ferromagnetism when the number of particles is the same as the degeneracy. We show that the occurrence of ferromagnetism is equivalent to the irreducibility of the projection matrix onto the space of single-particle ground states. We also demonstrate that this result can be exploited to establish a rigorous result for the ferromagnetic SU($N$) Kondo lattice model with a flat band. Specifically, we prove that when the SU($N$) Hubbard model is ferromagnetic, the ferromagnetic SU($N$) Kondo lattice model with the same hopping matrix also exhibits SU($N$) ferromagnetism.

25 pages, 3 figures, minor updates, 3 figures added

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Tools for quantum simulation with ultracold atoms in optical lattices
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling
• Direct observation of coherent inter-orbital spin-exchange dynamics
• Exact many-electron ground states on the diamond Hubbard chain
• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• Nagaoka states in the SU($n$) Hubbard model
• Flat bands in Weaire-Thorpe model and silicene
• Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly flat bands
• Methods for constructing parameter-dependent flat band lattices
• Ferromagnetism in the SU(N) Kondo lattice model -- SU(N) double exchange and supersymmetry
• Exact results for itinerant ferromagnetism in a $t_{2g}$ orbital system on cubic and square lattices
• Ferromagnetism in the Hubbard model with a gapless nearly-flat band

Cited by in corpus (2)

• Many-body Physics of Ultracold Alkaline-Earth atoms with SU($N$)-symmetric interactions
• Itinerant ferromagnetism in an SU(3) Fermi-Hubbard model at finite temperatures: A dynamical mean-field theory study