  We study a model in (2+1)-dimensional spacetime that is realized by an array
of chains, each of which realizes relativistic Majorana fields in
(1+1)-dimensional spacetime, coupled via current-current interactions. The
model is shown to have a lattice realization in an array of two-leg quantum
spin-1/2 ladders. We study the model both in the presence and absence of
time-reversal symmetry, within a mean-field approximation. We find regimes in
coupling space where Abelian and non-Abelian spin liquid phases are stable. In
the case when the Hamiltonian is time-reversal symmetric, we find regimes where
gapped Abelian and non-Abelian chiral phases appear as a result of spontaneous
breaking of time-reversal symmetry. These gapped phases are separated by a
discontinuous phase transition. More interestingly, we find a regime where a
non-chiral gapless non-Abelian spin liquid is stable. The excitations in this
regime are described by relativistic Majorana fields in (2+1)-dimensional
spacetime, much as those appearing in the Kitaev honeycomb model, but here
emerging in a model of coupled spin ladders that does not break SU(2)
spin-rotation symmetry.
