Ferromagnetism in the SU(n) Hubbard model with nearly flat band*

Recently, the SU(n) (n>2) Hubbard model describing multi-component fermions with SU(n) symmetry has been a focus of interest, as it is expected to exhibit a rich phase diagram. However, very little is known rigorously about the model with n>2. Here we study the model on a one-dimensional Tasaki lattice and derive rigorous results for the ground states. We first study the model with a flat band at the bottom of the single-particle spectrum. We prove that the ground states are SU(n) ferromagnetic when the number of particles is half the number of lattice sites, generalizing the previous result in Ref. [1]. To discuss SU(n) ferromagnetism in a non-singular setting, we perturb the flat-band model and make the bottom band dispersive. Then we find that SU(n) ferromagnetism in the ground states of the perturbed model at the same filling can be proved if each local Hamiltonian (independent of the system size) is positive semi-definite (p.s.d.). Furthermore, we prove that the local Hamiltonian is p.s.d. for sufficiently large interaction and band gap [2].
[1] R.-J. Liu, et al., arXiv:1901.07004 (2019).
[2] K. Tamura and H. Katsura, arXiv:1908.06286 (2019).