) Hubbard models with nearly flat bands*

The SU(n) Hubbard model, which describes multi-component fermions with SU(n) symmetric interaction, has attracted much attention recently because of its realization in cold-atom setups[1]. However, there are few rigorous results established for this model with n>2.
We study a class of SU(n) Hubbard models on d (>2)-dimensional decorated lattices and present rigorous results for the ground states [2]. We first consider the model with a flat band at the bottom of the single-particle spectrum and prove that the ground states are SU(n) ferromagnetic and unique, provided that the on-site Coulomb interaction is repulsive and the number of particles is the same as the number of unit cells. We then study a perturbed model by adding particular hopping terms that make the bottom band dispersive. We prove that the ground states of the model remain SU(n) ferromagnetic at the same filling when the band width of the lowest band is sufficiently narrow and the Coulomb repulsion is sufficiently large.
[1] S. Taie et al., Nat. Phys. 8, 825 (2012)
[2] K. Tamura and H. Katsura, arXiv:2009.03580 (2019)