Quantum spin structures and phase separation in the Hubbard model

In this thesis we focus on a systematic study of the ground state of the one-dimensional one-band Hubbard model in the Hartree–Fock approximation. Phases with non-uniform charge density and states with coexisting phases separated by a domain wall are included in the study. We calculate the full Hartree–Fock phase diagram for uniform and non-uniform phases, and we show that at particular electron densities the uniform phase is unstable to phase separation. Supercell calculations are carried out, and we use the computational minimisation procedure to calculate the Hartree–Fock energies for the self-consistent spin configurations.