Key points are not available for this paper at this time.
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 U₂ (the value at the transition), which depends strongly on the coordination number z and on N, the number of degenerate orbitals, that we vary from N=2 to 6 in our simulations. We prove that U₂ is a nondecreasing 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 U₂. Complementary, we explore the effect of long-range hopping on the appearance of itinerant ferromagnetism, and we demonstrate that it acts as an increased coordination number, protecting the ferromagnetic phase at small U. Finally, the effects of both the presence of some additional holes and the finite size of the clusters are briefly discussed.
Botzung et al. (Mon,) studied this question.