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.