  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 (0< n < 1.75) electron density when
the interactions are sufficiently strong. Quasi-long-range order of triplet
superconductivity coexists with the ferromagnetic order for a strong Hund
coupling region, where the inter-orbital interaction U'-J is attractive. At
quarter-filling (n=1), the insulating ferromagnetic state appears accompanying
orbital quasi-long-range order. For low densities (n<1), 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 (n>1), the phase diagram of the ferromagnetic phase is similar to
that obtained in infinite dimensions. In this case, the double exchange
mechanism is operative to stabilize 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<n<1.75 and phase separation occurs for
n just below the half-filling (n=2).
