Dimerized and trimerized phases for spin-2 bosons in a one-dimensional optical lattice

We study the phase diagram for spin-2 bosons loaded in a one-dimensional optical lattice. By using the 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 also can be easily implemented in experiments. By using the scattering lengths in the literature we estimate that (83)Rb, (23)Na, and (87)Rb can be ferromagnetic, dimerized, and trimerized, respectively