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We add a Heisenberg interaction term \alpha \lambda  in the one-dimensional SU(2) \otimes  XY spin-orbital model introduced by Kumar. At \lambda = 0  the spin and orbital degrees of freedom can be separated by a unitary transformation leading to an exact solution of the model. We show that a finite \lambda > 0 leads to spontaneous dimerization of the system which in the thermodynamic limit becomes a smooth phase transition at \lambda \rightarrow 0, whereas it remains discontinuous within the first-order perturbation approach. We present the behavior of the entanglement entropy, energy gap, and dimerization order parameter in the limit of \lambda \rightarrow 0 confirming the critical behavior. Finally, we show the evidence of another phase transition in the Heisenberg limit, \lambda \rightarrow \infty, and give a qualitative analytical explanation of the observed dimerized states both in the limit of small and large \lambda

Second-order Peierls transition in the spin-orbital Kumar-Heisenberg model