  We study the phase diagram for spin-2 bosons loaded in a one-dimensional
optical lattice. By using non-Abelian density matrix renormalization group
(DMRG) method we identify three possible phases: ferromagnetic, dimerized, and
trimerized phases. We sketch the phase boundaries based on DMRG. We illustrate
two methods for identifying the phases. The first method is based on the
spin-spin correlation function while in the second method one observes the
excitation gap as a dimerization or a trimerization superlattice is imposed.
The advantage of the second method is that it can also be easily implemented in
experiments. By using the scattering lengths in the literature we estimate that
$^{83}$Rb, $^{23}$Na, and $^{87}$Rb be ferromagnetic, dimerized, and trimerized
respectively.
