text: x  x 
  y  y 
  z  z  z 
  x  x  x  x 
  y  y  y 
  z  z  z  z 
  x  x  x  x 
  y  y  y 
  z  z  z  z 
  x  x  x 
  y  y  y 
  
  FIG. 1: The honeycomb lattice for the Kitaev model. Filled 
  and open circles indicate two sublattices. x, y, z label the links 
  along three diﬀerent directions used in (1). 