Numerical Studies of a Spin(4) Symmetric Spin Model

We numerically investigate a model with a projective SO(4) symmetry, analogous to the well-studied half-integer Heisenberg model with a projective SO(3) symmetry. The model is sign-problem free and can thus be studied in d>1 dimensions using Quantum Monte Carlo (QMC). Moreover, analytic arguments demonstrate the necessity of at least one quantum phase transition between two points in parameter space in 1d, interpolating between a Wess-Zumino-Witten k=1 state with a spontaneously broken Ζ₂ symmetry and valence bond solid (VBS) state. We provide the phase diagrams for the model in both 1d and 2d.