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The Kitaev model has recently attracted considerable attention in broad areas of research, such as condensed matter physics, statistical physics, and quantum information. This model is originally defined on a honeycomb lattice, and is exactly solvable due to the Ising conserved quantities on each hexagon. One of the most interesting properties of this model is that gapless and gapped quantum spin liquid (QSL) phases are stabilized at zero temperature by changing the exchange constants. In this study, we investigate a three-dimensional (3D) extension of the Kitaev model [1,2,3]. This model is relevant to the recently found Ir oxides Li2IrO3. Using a quantum Monte Carlo simulation that we newly developed, we analyze the thermodynamic properties in the 3D Kitaev model. We find that the model exhibits a finite-temperature phase transition between the QSLs and paramagnet in the whole parameter range. This result indicates that both gapless and gapped QSL phases at low temperatures are always distinguished from the high-temperature paramagnet by a phase transition. We also find that the transition is characterized by the topological nature of excitations, which is difficult to understand within the conventional Gintzburg-Landau-Wilson framework. This work has been done in collaboration with Y. Motome and M. Udagawa in Univ. of Tokyo.

[1] J. Nasu, T. Kaji, K. Matsuura, M. Udagawa, and Y. Motome, Phys. Rev. B 89, 115125 (2014).
[2] J. Nasu, M. Udagawa, and Y. Motome, Phys. Rev. Lett. 113, 197205 (2014).
[3] J. Nasu, M. Udagawa, and Y. Motome, preprint (arXiv:1409.4865).

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