Non-Abelian Spin Liquid in a Spin-One Quantum Magnet

We study a time-reversal invariant non-Abelian spin-liquid state in an $SU(2)$ symmetric spin $S=1$ quantum magnet on a triangular lattice. The spin liquid is obtained by quantum disordering a noncollinear nematic state. We show that such a spin liquid cannot be obtained by the standard projective construction for spin liquids. We also study the phase transition between the spin liquid and the noncollinear nematic state and show that it cannot be described within the Landau-Ginzburg-Wilson paradigm.

Figure 1

The ordered state of the three-sublattice nematic state. The directors on the three sublattices are shown as three orthogonal differently colored rods (black, red, and blue). As discussed in the text, one may also define the order-parameter space in terms of spinons $z$, which reside at the vertices of a bigger auxiliary triangular lattice. We take the vertices of this auxiliary triangular lattice (marked as ×) to lie at the centroid of every third triangular plaquette of the original lattice.