  We analyse a spin-1/2 chain with two-spin interactions which shown to exactly
solvable by Lieb, Schultz and Mattis. We show that the model can be viewed as a
generalised Kitaev model that is analytically solvable for all defect sectors.
We present an alternate proof that the defect free sector is the ground state,
which is valid for a larger parameter range. We show that the defect sectors
have degenerate ground states corresponding to unpaired Majorana fermion modes
and that the degeneracy is topologically protected against disorder in the
spin-spin couplings. The unpaired Majorana fermions can be manipulated by
tuning the model parameters and can hence be used for topological quantum
computation.
