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The exactly solvable Kitaev honeycomb lattice model is realized as the lowenergy effect Hamiltonian of a spin-1/2 model with spin rotation andtime-reversal symmetry. The mapping to low energy effective Hamiltonian isexact, without truncation errors in traditional perturbation series expansions.This model consists of a honeycomb lattice of clusters of four spin-1/2moments, and contains short-range interactions up to six-spin(or eight-spin)terms. The spin in the Kitaev model is represented not as these spin-1/2moments, but as pseudo-spin of the two-dimensional spin singlet sector of thefour antiferromagnetically coupled spin-1/2 moments within each cluster. Spincorrelations in the Kitaev model are mapped to dimer correlations orspin-chirality correlations in this model. This exact construction is quitegeneral and can be used to make other interesting spin-1/2 models from spinrotation invariant Hamiltonians. We discuss two possible routes to generate thehigh order spin interactions from more natural couplings, which involvesperturbative expansions thus breaks the exact mapping, although in a controlledmanner.

Realization of the Exactly Solvable Kitaev Honeycomb Lattice Model in a Spin Rotation Invariant System