Spin density wave selection in the one-dimensional Hubbard model

The Hartree-Fock ground-state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree-Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform DSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground-state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher-dimensional Hubbard models and the J(1)-J(2) Heisenberg model.