Phase separation in a t-J model

We study a simple extension of the Heisenberg model that is abstracted from the large-U limit of the Hubbard Hamiltonian and includes charge fluctuations. An attempt is made to elucidate some basic features of the T=0 phase diagram within a suitable 1/N expansion. We find that the ferromagnetic boundary dictated by a naive application of the Nagaoka theorem is actually incorrect because of an instability induced by phase separation. We derive what we believe to be the correct ferromagnetic boundary for sufficiently high dimension, and provide a detailed description of the ensuing phase separation. We also find that a uniform canted antiferromagnetic state is stable over a nontrivial region of the phase diagram. Potential implications of these results for the physics of the original Hubbard model are briefly discussed.