text: In this Section we will use directly the results of the 
  previous Section to write down a Hamiltonian whose low 
  energy sector is described by the Kitaev model. The 
  Hamiltonian will be constructed on the physical spin lat- 
  tice illustrated in FIG. 2. 
  In this Section we will use 
  j, k to label four-spin clusters (pseudo-spin-1/2 sites), the 
  physical spins in cluster j are labeled as Sj1, . . . , Sj4. 
  Apply the mappings developed in Section II, we have 