The Kitaev model on the honeycomb lattice has been receiving substantial attention due to the discovery of quantum spin liquid state associated with this model. Consequently, its classical partners such as the Kitaev-Heisenberg (KH) model and associated phase transitions become concerned. Specifically, an intermediate Kosterlitz-Thouless (KT) phase engaged in the transition from the high-temperature ($T$) disordered state to the low-$T$ sixfold degenerate state is predicted in the isotropic KH model [Phys. Rev. Lett. 109, 187201 (2012)], but so far no sufficient experimental proof has been reported. In this work, we consider an essential extension of this KH model on the honeycomb lattice by including the Kitaev exchange anisotropy that is non-negligible in realistic materials. The associated phase transitions are thus investigated using the Monte Carlo simulations. It is found that such an anisotropy will result in a degradation of the sixfold degeneracy of the ground state in the isotropic KH model down to the fourfold or twofold degenerate ground state, and the finite-$T$ phase transitions will also be modified remarkably. Interestingly, the intermediate KT phase can be suppressed by this Kitaev exchange anisotropy. This work thus provides a more realistic description of the physics ingredient with the KH model and presents a possible explanation on absence of the intermediate phase in real materials where the Kitaev exchange anisotropy can be more or less available.

中文翻译：

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经典交换各向异性Kitaev-Heisenberg模型中的相变

由于发现了与该模型相关的量子自旋液态，因此蜂窝状晶格上的Kitaev模型受到了广泛的关注。因此，它的经典合作伙伴（例如Kitaev-Heisenberg（KH）模型）和相关的相变变得令人关注。具体而言，中间的Kosterlitz-Thouless（KT）相参与了从高温（$Ť$）无序状态到低$Ť$在各向同性KH模型中预测了六倍简并状态。牧师 109，187201（2012）]，但到目前为止，还没有足够的实验证明有报道。在这项工作中，我们考虑通过在实际材料中不可忽略的Kitaev交换各向异性来在蜂窝网格上对该KH模型进行必要的扩展。因此，使用蒙特卡洛模拟研究了相关的相变。发现这种各向异性将导致各向同性KH模型中基态的六倍简并性下降到四倍或两倍的简并基态，而有限元$Ť$相变也将显着改变。有趣的是，中间的KT相可以通过该Kitaev交换各向异性来抑制。因此，这项工作为KH模型提供了对物理成分的更现实的描述，并提出了关于在实际材料中不存在中间相的可能解释，在该情况下，Kitaev交换各向异性或多或少可以得到。