Critical properties of the Kitaev-Heisenberg model

Abstract

We study critical properties of the Kitaev-Heisenberg model on the honeycomb lattice at finite temperatures which might describe the physics of the quasi two-dimensional compounds, Na${}_2$IrO${}_3$ and Li${}_2$IrO${}_3$. The model undergoes two phase transitions as a function of temperature. At low temperature, thermal fluctuations induce magnetic long-range order by order-by-disorder mechanism. Magnetically ordered state with the spontaneously broken $Z_6$ symmetry persists up to a certain critical temperature. We find that there is an intermediate phase between the low-temperature ordered phase and the high-temperature disordered phase. The finite-sized scaling analysis suggests that the intermediate phase is a critical Kosterlitz-Thouless phase with continuously variable exponents. We argue that the intermediate phase has been actually observed above the low-temperature magnetically ordered phase in Na${}_2$IrO${}_3$, and likely in Li${}_2$IrO${}_3$.

5 pages, 6 figures

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