Phase separation in the one-dimensional 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, extending the results presented in cond-mat/9511116. This allows antiferromagnetism, saturated ferromagnetism, spiral spin density waves and a collinear structure with unit cell $\uparrow \uparrow \downarrow \downarrow$. 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.