Unfortunately, the global spin rotation symmetry is not essential for the spin liquid in the general sense. The defining property of the spin liquid is the **intrinsic topological order** (or the **quantum order** for gapless spin liquid). The Kitaev spin liquid possesses the $\mathbb{Z}_2$ topological order, which makes it a spin liquid, although the spin rotation symmetry is explicitly broken even on the model level. Of cause, you may restrict the discussion to the spin rotational symmetric cases, i.e. the spin-SU(2) symmetric spin liquid, which is just a subclass of all spin liquids, and indeed Kitaev spin liquid does not belong to this subclass. However, it is possible to write down a variation of the Kitaev model which is spin-SU(2) symmetric, and the resulting ground state is a rotational symmetric spin liquid.

This post imported from StackExchange Physics at 2014-03-09 08:45 (UCT), posted by SE-user Everett You