Numerical observation of SU (N) Nagaoka ferromagnetism

We provide numerical evidence of the Nagaoka's theorem in the SU (N) Fermi-Hubbard model on various cluster geometries, such as the square, the honeycomb and the triangular lattices. In particular, by diagonalizing several finite-size clusters, we show that for one hole away from filling 1/N, the itinerant ferromagnetism arises for U (the positive on-site interaction) larger than Uc (the value at the transition), which strongly depends on the coordination number z and on N, the number of degenerate orbitals, that we vary from N=2 to N=6 in our simulations. We prove that Uc is a non decreasing function of N. In addition, we find that the lattice dependency is rooted in the kinetic energy of the hole. We find that large coordination numbers z lower the value of Uc. Complementary, we explore the effect of long-range hopping on the appearance of itinerant ferromagnetism and demonstrate that it acts as an increased coordination number, protecting the ferromagnetic phase at small U. Finally, both the effects of the presence of some additional holes and of the finite size of the clusters are briefly discussed.