Two Step Restoration of SU(2) Symmetry in a Frustrated Quantum Magnet

We demonstrate the existence of a spin-nematic, moment-free phase in a quantum four-spin ring exchange model on the square lattice. This unusual quantum state is created by the interplay of frustration and quantum fluctuations which lead to a partial restoration of $SU(2)$ symmetry when going from a four- sublattice orthogonal biaxial N\'eel order to this exotic uniaxial magnet. A further increase of frustration drives a transition to a fully gapped $SU(2)$ symmetric valence bond crystal.