  We introduce a simple lattice spin model that is written in terms of the
well-known four-dimensional $\gamma$-matrix representation of the Clifford
algebra. The local spins with a four-dimensional Hilbert space transform in a
spinorial $(1/2,0) \oplus (0,1/2)$ representation of $SO(4)$, a symmetry of our
model. When studied on a chain, and as a function of a transverse field tuning
parameter, our model undergoes a quantum phase transition from a valence bond
solid phase to a critical phase that is described by an $SU(2)_1$ WZW field
theory.
