Spin rotation ($U(\mathbf{\theta })=e^{-i\mathbf{\theta }\cdot \mathbf{S}}$)

A spin rotation acts on a quantum state through the unitary representation generated by its angular momentum operators. With $\hslash =1$, rotation by angle $\theta$ about axis $\hat{\mathbf{n}}$ is $e^{-i\theta \hat{\mathbf{n}}\cdot \mathbf{S}}$. Simultaneously rotating every site is a global symmetry of an isotropic Heisenberg model.