  We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2
chain, which is a one-dimensional generalization of the two dimensional Kitaev
honeycomb model. Using the mean field theory, coupled with a gauge fixing
procedure to implement the single occupancy constraint, we obtain the phase
diagram of the model. We then show that it matches the exact results obtained
earlier using the Majorana fermion representation. We also compute the
spin-spin correlation in the gapless phase and show that it is a spin liquid.
Finally, we map the one-dimensional model in terms of the slave fermions to the
model of 1D p-wave superconducting model with complex parameters and show that
the parameters of our model fall in the topological trivial regime and hence
does not have edge Majorana modes.
