Correlated spin and orbital dimerizations in spin-orbital models

We study a one-dimensional spin-orbital model with Heisenberg symmetry for spins and XY symmetry for orbital degrees of freedom. We establish the grou nd-state phase diagram of this model. The gapless phases of the model consi st of fully polarized ferromagnetic spin states together with the filled Jo rdan-Wigner Fermi sea for the orbitals. Two such phases, with ferromagnetic and antiferromagnetic XY correlations for the orbitals, are found. All oth er phases are found to have a spin gap with degenerate ground states. Two t ypes of correlated spin and orbital dimerizations are observed: (i) spin si nglet with orbital singlet in alternating rungs and (ii) spin singlet with orbital triplet in the same rung. The phase boundaries, energy gaps, and or der parameters are evaluated using the density matrix renormalization group method.