Holes in the infinite-U Hubbard model: Instability of the Nagaoka state

The solution of a three-body Schrödinger equation (for two holes and a spin flip) shows that in the U=∞ Hubbard model the saturated ferromagnetic state with two holes is unstable (in a finite volume and for periodic boundary conditions). The ground state carries a finite momentum, and becomes degenerate with the Nagaoka state in the thermodynamic limit. This is in agreement with exact diagonalization results for small lattices where, in addition, we find that the true two-hole ground state is a singlet. As a result, our notions of ferromagnetism in the Hubbard model might need revision.