Ferromagnetism in Doubly Degenerate Hubbard Models near Quarter-Filled Band(Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties)

概要

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Ferromagnetism of the Hubbard models with doubly degenerate orbitals is studied in the case of infinitely large intra-atomic Coulomb interactions. It is assumed that the hopping of electrons occurs between the same orbitals of the nearest-neighbor sites, and the band is almost quarter-filled or N_e=N-1, where N_e and N are the total number of electrons and the total number of the atomic sites, respectively. It is rigorously proved that the ground state energy is highly degenerate for any dimension and for any lattice structure. Not only states with the maximum total spin (S spin) and the total orbital spin (T spin) but also certain states with smaller total S and T spins have the same ground state energy. The degeneracy originates from the high symmetry of the hopping matrix elements. The introduction of off-diagonal hoppings between different orbitals makes the ground state unique, which becomes ferromagnetic with the maximum total S and T spins as well as T_x for simple-cubic, body-centered-cubic, and face-centered-cubic lattices with positive hopping matrix elements. For the proof Nagaoka's theorem for the single-orbital Hubbard model and the connectivity of the basis states were used.
社団法人日本物理学会の論文
2006-04-15