Phase separation in Hubbard model

The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated in the mu-U plane, restricted to phases with no charge density modulation. This allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves and a collinear structure with unit cell up arrow up arrow down arrow down arrow. The spiral phase is unstable against phase separation near quarter-, half-and three-quarter-filling. For large U this occurs at hole (or electron) doping of (3t/pi(2) U)(1/3) from half-filling