Critical properties of the Kitaev-Heisenberg model
A prominent example of anisotropic spin-orbital models is the Kitaev-Heisenberg (KH) model on
the honeycomb lattice [1,2]. This model was proposed as the minimal model to describe the low-
energy physics of the quasi two-dimensional compounds, Na2IrO3 and Li2IrO3. In these compounds,
Ir4+ ions are in a low spin 5d5 conguration and form weakly coupled hexagonal layers. Due to
strong SOC, the atomic ground state is a doublet where the spin and orbital angular momenta of Ir4+
ions are coupled into Je
= 1=2. The KH model describing the interactions between Je
contains two competing nearest neighbor interactions: an isotropic antiferromagnetic Heisenberg
exchange interaction originated mainly from direct direct overlap of Ir t2g orbitals and a highly
anisotropic Kitaev exchange interaction  which originates from hopping between Ir t2g and O 2p
orbitals via the charge-transfer gap.
We study critical properties of the KH model on the honeycomb lattice at nite temperatures [4,5].
The model undergoes two phase transitions as a function of temperature. At low temperature,
thermal uctuations induce magnetic long-range order by order-by-disorder mechanism. This mag-
netically ordered state with a spontaneously broken Z6 symmetry persists up to a certain critical
temperature. We nd that there is an intermediate phase between the low-temperature, ordered
phase and the high-temperature, disordered phase. Finite-size 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 likely observed above the magnetically ordered phase
in A2IrO3 compounds.
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 J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010).
 A. Kitaev, Ann. Phys. 321, 2 (2006).
 C. Price and N. B. Perkins, Phys. Rev. Lett. 109, 187201 (2012).
 C. Price and N. B. Perkins, Phys. Rev. B 88, 024410 (2013).