Nagaoka ferromagnetism in large-spin fermionic and bosonic systems

We study the magnetic properties of itinerant quantum magnetic particles, described by a generalized Hubbard model with large spin (S>1/2), which may be realized in optical lattices of laser-cooled atom systems. In fermion systems (half-integer spins), an extended form of Nagaoka ferromagnetism may be realized. However, as novel aspects of the large-spin cases, we found that the condition on the lattice connectivity is more stringent than in the case of S=1/2 particles and that the system shows a peculiar degenerate structure of the ground state in which the ferromagnetic state is included. In contrast, it turns out that the ground state of itinerant bosonic systems (integer spins) has a degenerate structure similar to that of fermion system with S>1/2 regardless of the shape, connectivity, or filling of the lattice, and that the state with the maximum total spin is always one of the ground states. Because the system consists of 2S+1 types of particles and we study a SU(2S+1) invariant model, the degeneracy of the ground state is given by the multiplets of the fully symmetric Young tableau of SU(2S+1) if the state with maximum total spin belongs to the ground state.