text: We constructed the exactly solvable Kitaev honeycomb 
  model1 as the exact low energy eﬀective Hamiltonian of 
  a spin-1/2 model [equations (8) or (9)] with spin-rotation 
  and time reversal symmetry. The spin in Kitaev model is 
  represented as the pseudo-spin in the two-fold degenerate 
  spin singlet subspace of a cluster of four antiferromag- 
  netically coupled spin-1/2 moments. The physical spin 
  model is a honeycomb lattice of such four-spin clusters, 
  with certain inter-cluster interactions. The machinery 
  for the exact mapping to pseudo-spin Hamiltonian was 
  developed (see e.g. TABLE I), which is quite general 
  and can be used to construct other interesting (exactly 
  solvable) spin-1/2 models from spin rotation invariant 
  systems. 
  
  The generic couplings in (A1) [second term] can be 
  converted to couplings to these orthogonal modes, 
  
  where Q are generalized coordinates of the corresponding 
  modes, functions f can be read oﬀ from TABLE 1.2 of 
  Ref.35. For the A mode, δrℓm =  2/3QA, so f A is 
  p 
  
  f A = 