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              [html]<thead><tr><td>II. Formulation of the Pseudo - spin - 1 / 2 from Four - spin Cluster.</td><td>III. Realization of the Kitaev Model.</td></tr></thead><tbody><tr><td>3</td><td>IV. Generate the High Order Physical Spin</td></tr><tr><td>Interactions by Perturbative Expansion. A. Generate the High Order Terms by Coupli</td><td>5</td></tr><tr><td>to Optical Pluonon.</td><td>5</td></tr><tr><td>B. Generate the High Order Terms by Magnetic Interactions between Clusters.</td><td>τ</td></tr><tr><td>V. Conclusions.</td><td>8</td></tr><tr><td>Acknowledgments</td><td>8</td></tr><tr><td>A. Coupling between Distortions of a Tetrahedron and the Pseudo - spins</td><td>8</td></tr><tr><td>B. Derivation of the Terms Generated by Second Order Perturbation of Inter - cluste Magnetic Interactions</td><td>9</td></tr><tr><td>References</td><td>10</td></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr><tr></tr></tbody>
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