Topological Order in an Entangled SU(2)$\otimes$XY Spin-Orbital Ring

We present rigorous topological order which emerges in a one-dimensional spin-orbital model due to the ring topology. Although an exact solution of a spin-orbital ring with SU(2) spin and XY orbital interactions separates spins from orbitals by means of a unitary transformation, the spins are not independent when the ring is closed, but form two half-rings carrying opposite pseudomomenta. We show that an inverse transformation back to the physical degrees of freedom entangles the spin half-rings with the orbitals once again. This surprising correlation arises on changing the topology from an open to a closed chain, which reduces the degeneracy of the ground-state manifold, leaving in it only the states in which pseudomomenta compensate each other.