Ferromagnetism in the one-dimensional Hubbard model with orbital degeneracy: From low to high electron density

We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high $\mathrm{}(0<n<\mathrm{}1.75\mathrm{})\mathrm{}$ electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction $U^{\prime }-J$ is attractive. At quarter-filling $\mathrm{}(n=1\mathrm{}),$ the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities $\mathrm{}(n<\mathrm{}1\mathrm{}),$ ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities $\mathrm{}(n>\mathrm{}1\mathrm{}),$ the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\lesssim n\lesssim 1.75$ and phase separation occurs for n just below the half-filling $\mathrm{}(n=2\mathrm{}).$