Non-Abelian statistics and a hierarchy of fractional spin liquids in spin-$S$ antiferromagnets

We propose a hierarchy of spin liquids with spin $S$, which are generated via a Schwinger boson projection from $2S$ (Abelian) chiral spin liquids with $S=1/2$. We argue that the P and T invariant liquids we construct for integer spin $S$ support SU(2) level $k=S$ non-Abelian statistics. We conjecture that these spin liquids serve as paradigms for antiferromagnets which are disordered through mobile charge carriers.

Figure 1

We create a spin $S=1$ liquid out of two $S=1/2$ CSLs by projection onto the symmetric spin configuration on each site. Schwinger bosons ensure this is done automatically when multiplying the liquids.