text: in terms of physical spins S, has full 
  spin rotation symmetry and time-reversal symmetry. A 
  pseudo-magnetic ﬁeld term 
  ~τj term can also be 
  included under this mapping, however the resulting Ki- 
  taev model with magnetic ﬁeld is not exactly solvable. 
  It is quite curious that such a formidably looking Hamil- 
  tonian (8), with biquadratic and six-spin(or eight-spin) 
  terms, has an exactly solvable low energy sector. 
  
  This model, 
  
  ~h 
  Pj  · 