The Kitaev model of spin-1/2 on a honeycomb lattice supports degenerate topological ground states and may be useful in topological quantum computation. Na$_{2}$IrO$_{3}$ with honeycomb lattice of Ir ions have been extensively studied as candidates for the realization of the this model, due to the effective $J_{text{eff}}=1/2$ low-energy excitations produced by spin-orbit and crystal-field effect. As the eventual realization of Kitaev model has remained evasive, it is highly desirable and challenging to tune the candidate materials toward such end. It is well known external pressure often leads to dramatic changes to the geometric and electronic structure of materials. In this work, the high pressure phase diagram of Na$_{2}$IrO$_{3}$ is examined by first-principles calculations. It is found that Na$_{2}$IrO$_{3}$ undergoes a sequence of structural and magnetic phase transitions, from the magnetically ordered phase with space group $C2/m$ to two bond-ordered non-magnetic phases. The low-energy excitations in these high-pressure phases can be well described by the $J_{text{eff}}=1/2$ states.
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