Lattice spin models for non-Abelian chiral spin liquids

We suggest a class of two-dimensional lattice spin Hamiltonians describing non-Abelian SU(2) chiral spin liquids—spin analogs of fractional non-Abelian quantum Hall states—with gapped bulk and gapless chiral edge excitations described by the SU(2)${}_n$ Wess-Zumino-Novikov-Witten conformal field theory. The models are constructed from an array of generalized spin-$n/2$ ladders with multi-spin-exchange interactions which are coupled by isolated spins. Such models allow a controllable analytic treatment starting from the one-dimensional limit and are characterized by a bulk gap and non-Abelian SU(2)${}_n$ gapless edge excitations.

Figure 1

The spin arrangement for the suggested model. Different link colors correspond to different exchange interactions. The blue links mark the strongest isotropic exchange $J$, the red ones mark weaker isotropic exchange $J^{\prime }$, the green links correspond to the anisotropic interladder exchange, and the magenta ones to the Ising-like anisotropic exchange $I^{ab}$ between intermediate spins. The blue arrows denote the three-spin-exchange interactions. Since there is no static spin order, all spin orientations depicted on the figure should be ignored.