Critical properties of the Kitaev-Heisenberg Model

Collective behavior of local moments in Mott insulators in the presence of strong spin-orbit coupling is one of the most interesting questions in modern condensed matter physics. Here we study the finite temperature properties of the Kitaev-Heisenberg model which describe the interactions between the pseudospin $J= 1/2$ iridium moments on the honeycomb lattice. This model was suggested as a possible model to explain low-energy physics of AIr$_2$O$_3$ compounds. In our study we show that the Kitaev-Heisenberg model may be mapped into the six state clock model with an intermediate power-law phase at finite temperatures. In the framework of the Ginsburg-Landau theory, we provide an analysis of the critical properties of the finite-temperature ordering transitions.