  We analyze the Kitaev model on the triangle-honeycomb lattice whose ground
state has recently been shown to be a chiral spin liquid. We consider two
perturbative expansions: the isolated-dimer limit containing Abelian anyons and
the isolated-triangle limit. In the former case, we derive the low-energy
effective theory and discuss the role played by multi-plaquette interactions.
In this phase, we also compute the spin-spin correlation functions for any
vortex configuration. In the isolated-triangle limit, we show that the
effective theory is, at lowest nontrivial order, the Kitaev honeycomb model at
the isotropic point. We also compute the next-order correction which opens a
gap and yields non-Abelian anyons.
