An exact chiral spin liquid with non-Abelian anyons

We establish the existence of a ``chiral spin liquid'' (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle [1]. This state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSL's separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial CSL (Chern number $\pm 1$) obey non-Abelian statistics. \\ $[1]$ Hong Yao and Steven A. Kivelson, Phys. Rev. Lett. in Press.