Transverse Field ${\hat{I}}^3$-Matrix Spin Chains

Abstract

We introduce a simple lattice spin model that is written in terms of the well-known four-dimensional ${\hat{I}}^3$-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.

12 pages, 9 figures; added references for section 2, corrected a typo in appendix D