Symmetry Classes of Spin and Orbital Ordered States in a Triply Degenerate t_<2g> Hubbard Model(Condensed Matter and Statistical Physics)

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We describe symmetry properties of spin and orbital unrestricted Hartree-Fock(HF) solutions in a triply degenerate t_<2g> Hubbard model on a three-dimensional cubic lattice. We present a short review of the group theoretical bifurcation theory of the HF equation. Using this bifurcation theory, we obtain all types of broken symmetry solutions which bifurcate from the normal state through one-step transition in the cases of ordering vectors Q_0=(0, 0, 0) and Q_1=(π, π, π). These states are 7 types of nonmagnetic orbital ordered states with the ordering vector Q_0, 9 types nonmagnetic orbital ordered states with the ordering vector Q_1, 9 types ferromagnetic orbital ordered states with the ordering vector Q_0 and 9 types antiferromagnetic orbital ordered states with the ordering vector Q_1. We also illustrate a method to obtain states bifurcating through two-step transitions from the normal state. We present a general method to determine the canonical form of the HF Hamiltonian and the occupied atomic orbitals from the isotropy subgroup of a state. With the above-described procedure we systematically derived states which have complex occupied atomic orbitals. We performed numerical calculations of these states for a particular parameter set.
理論物理学刊行会の論文
2007-09-25