Phase diagram of a one-dimensional spin-orbital model

We study a one-dimensional spin-orbital model using both analytical and numerical methods. Renormalization group calculations are performed in the vicinity of a special integrable point in the phase diagram with $\mathrm{SU}\left(4\right)\mathrm{}$ symmetry. These indicate the existence of a gapless phase in an extended region of the phase diagram, missed in previous studies. This phase is $\mathrm{SU}\left(4\right)\mathrm{}$ invariant at low energies apart from the presence of different velocities for spin and orbital degrees of freedom. The phase transition into a gapped dimerized phase is in a generalized Kosterlitz-Thouless universality class. The phase diagram of this model is sketched using the density matrix renormalization group technique.