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Quantum information approach to the quantum phase transition in the Kitaev honeycomb model

Kitaev honeycomb model with topological phase transition at zero temperature is studied using quantum information method. Based on the exact solution of the ground state, the mutual information between two nearest sites and between two bonds with longest distance are obtained. It is found that the mutual information show some singularities at the critical point where the ground state of the system transits from gapless phase to gapped phase. The finite-size effects and scalar behavior are also studied. The mutual information can serve as good indicators of the topological phase transition, since the mutual information catches some global correlation properties of the system. Meanwhile, this method has other advantages such that the phase transition can be determined easily and the order parameters are not required previously, for the order parameters of some topological phase transitions are hard to know.