Ferromagnetism in $d$-dimensional SU($n$) Hubbard models with nearly flat bands

Abstract

We present rigorous results for the SU(n) Fermi-Hubbard models with finite-range hopping in d (≥ 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 single-particle spectrum and prove that the ground states exhibit SU(n) ferromagnetism when the number of particles is equal to the number of unit cells. We then perturb the models by adding particular hopping terms and make the bottom bands dispersive. Under the same filling condition, it is proved that the ground states remain SU(n) ferromagnetic when the bottom bands are sufficiently flat and the Coulomb repulsion is sufficiently large. Keywords Hubbard model • Ferromagnetism • Nearly flat band 1 IntroductionRecent advances in experimental techniques have made it possible to simulate various quantum systems by using ultracold atoms in optical lattices [1,2,3,4]. Thanks to the controllability of lattice potentials and interaction strengths with high accuracy, ultracold atomic systems are expected to be a versatile tool for exploring many-body physics in strongly correlated systems. Of particular interest are multicomponent fermionic systems with alkaline earth-like atoms in cold-atom setups. Experimental realizations of such systems with SU(n) symmetric interactions have been reported in [5,6,7]. They are expected to be well described by the