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  Rousochatzakis, I.; Reuther, J.; Thomale, R.; Rachel, S.; Perkins, N.B.: Phase Diagram and Quantum Order by Disorder in the Kitaev K₁ - K₂ Honeycomb Magnet. Physical Review X 5 (2015), p. 041035/1-9

10.1103/PhysRevX.5.041035
Open Access Version

Abstract:
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling K₂, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na₂IrO₃, and may also play a role in α−RuCl₃ and Li₂IrO₃. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na₂IrO₃. Moreover, the minimal K₁ − K₂ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.