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Motivated by the work of Kitaev, we construct an exactly soluble spin-$\frac{1}2$ model on honeycomb lattice whose ground states are identical to $\Delta_{1x}p_x+\Delta_{1y}p_y+i(\Delta_{2x}p_x+\Delta_{2y}p_y)$-wave paired fermions on square lattice, with tunable paring order parameters.
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There are other gapless lines corresponding to 𝐩 ∗ = ( 0 , π ) {\bf p}^{*}=(0,\pi) and ( π , 0 ) (\pi,0) . The Pfaffian and anti-Pfaffian states may be discussed near these points. For the anti-Pfaffian, see, S. S. Lee, S. Ryu, C. Nayak, and M. P. A. Fisher, Phys. Rev. Lett. 99
2007
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D. H. Lee, G. M. Zhang, and T. Xiang, Phys. Rev. Lett. 99
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H. D. Chen and J. P. Hu, Phys. Rev. B 76
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K. P. Schmidt, S. Dusuel and J. Vidal, Phys. Rev. Lett. 100
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V. Lahtinen, G. Kells, A. Carollo, T. Stitt, J. Vala and J. K. Pachos, Ann. of Phys. 323
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