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We present a two-dimensional lattice model for quantum spin-1/2 for which thelow-energy limit is governed by four flavors of strongly interacting Majoranafermions. We study this low-energy effective theory using two alternativeapproaches. The first consists of a mean-field approximation. The secondconsists of a Random Phase approximation (RPA) for the single-particle Green'sfunctions of the Majorana fermions built from their exact forms in a certainone-dimensional limit. The resulting phase diagram consists of two competingchiral phases, one with Abelian and the other with non-Abelian topologicalorder, separated by a continuous phase transition. Remarkably, the Majoranafermions propagate in the two-dimensional bulk, as in the Kitaev model for aspin liquid on the honeycomb lattice. We identify the vison fields, which aremobile (they are static in the Kitaev model) domain walls propagating alongonly one of the two space directions.

A model of chiral spin liquids with Abelian and non-Abelian topological phases