text: However, in the original Kitaev model and its later 
  generalizations in the form of spin models, spin rotation 
  symmetry is explicitly broken. This makes them harder 
  to realize in solid state systems. There are many pro- 
  posals to realized the Kitaev model in more controllable 
  in cold atom optical lattices17,18, or in 
  situations, e.g. 
  superconducting circuits19. But it is still desirable for 
  theoretical curiosity and practical purposes to realize the 
  Kitaev-type models in spin rotation invariant systems. 
  
  tion III the Kitaev model will be explicitly constructed 
  using this formalism, and some properties of this con- 
  struction will be discussed. In Section IV we will discuss 
  two possible ways to generate the high order spin in- 
  teractions involved in the construction of Section III by 
  perturbative expansions. Conclusions and outlook will 
  be summarized in Section V. 
  
  In this paper we realize the Kitaev honeycomb lattice 
  model as the low energy Hamiltonian for a spin rotation 
  invariant system. The trick is not to use the physical spin 
  as the spin in the Kitaev model, instead the spin-1/2 in 
  Kitaev model is from some emergent two-fold degener- 
  ate low energy states in the elementary unit of physical 
  system. This type of idea has been explored recently by 
  Jackeli and Khaliullin20, in which the spin-1/2 in the Ki- 
  taev model is the low energy Kramers doublet created by 
  strong spin-orbit coupling of t2g orbitals. In the model 
  presented below, the Hilbert space of spin-1/2 in the Ki- 
  taev model is actually the two dimensional spin singlet 
  sector of four antiferromagnetically coupled spin-1/2 mo- 
  ments, and the role of spin-1/2 operators(Pauli matrices) 
  in the Kitaev model is replaced by certain combinations 
  Sℓ)] between the 
  of Sj · 
  four spins. 
  
  II. FORMULATION OF THE PSEUDO-SPIN-1/2 
  FROM FOUR-SPIN CLUSTER. 