  We investigate the ground-state property and the excitation gap of a
one-dimensional spin-orbital model with isotropic spin and anisotropic orbital
exchange interactions, which represents the strong-coupling limit of a
two-orbital Hubbard model including the Hund's rule coupling ($J$) at quarter
filling, by using a density-matrix renormalization group method. At J=0, spin
and orbital correlations coincide with each other with a peak at $q=\pi/2$,
corresponding to the SU(4) singlet state. On the other hand, spin and orbital
states change in a different way due to the Hund's rule coupling. With
increasing $J$, the peak position of orbital correlation changes to $q=\pi$,
while that of spin correlation remains at $q=\pi/2$. In addition, orbital dimer
correlation becomes robust in comparison with spin dimer correlation,
suggesting that quantum orbital fluctuation is enhanced by the Hund's rule
coupling. Accordingly, a relatively large orbital gap opens in comparison with
a spin gap, and the system is described by an effective spin system on the
background of the orbital dimer state.
