We analyze a spin-$1/2$ chain with two-spin interactions which are shown to be exactly solvable by Lieb, Schultz, and Mattis [Ann. Phys. 16, 407 (1961)]. We show that the model can be viewed as a generalized 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.

• Received 23 January 2013

DOI:https://doi.org/10.1103/PhysRevB.87.174414