Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
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DOI：
10.1103/physrevb.109.024439
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发表时间：
2023-11
影响因子：
3.7
通讯作者：
Aayush Vijayvargia;Urban F. P. Seifert;O. Erten
中科院分区：
文献类型：
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作者：
Aayush Vijayvargia;Urban F. P. Seifert;O. Erten
我们研究了双层Kitaev蜂窝模型与伊辛层间相互作用的相图，通过微扰理论推导出有效的模型，并进行马约拉纳平均场理论计算。我们发现，不同的阵列的磁性和拓扑相变发生，这取决于层间伊辛相互作用的方向和Kitaev相互作用的相对符号。当两个层具有相同的Kitaev相互作用符号时，发生从Kitaev自旋液体到磁有序状态的一级转变。磁序沿着伊辛轴指向，对于（反）铁磁Kitaev相互作用，磁序是（反）铁磁的.然而，当两个层有相反的迹象Kitaev相互作用，我们观察到一个显着的减弱磁有序的倾向和Kitaev自旋液体生存到一个显着更大的层间交换。我们的平均场分析表明，出现了一个中间带隙的$\mathbb{Z}_2$自旋液体状态，这最终变得不稳定的vison凝聚。受限相由高度受挫的罗盘模型描述。我们进一步利用微扰理论研究了Ising轴沿着$\hat{z}$-轴或位于$xy$-平面的模型。在这两种情况下，我们的分析揭示了一维伊辛链的形成，保持解耦的微扰理论，导致一个subextensive基态简并。我们的结果突出了双层量子自旋液体中拓扑有序和磁有序倾向之间的相互作用。
We investigate the phase diagram of a bilayer Kitaev honeycomb model with Ising interlayer interactions, deriving effective models via perturbation theory and performing Majorana mean-field theory calculations. We show that a diverse array of magnetic and topological phase transitions occur, depending on the direction of the interlayer Ising interaction and the relative sign of Kitaev interactions. When two layers have the same sign of the Kitaev interaction, a first-order transition from a Kitaev spin liquid to a magnetically ordered state takes place. The magnetic order points along the Ising axis and it is (anti)ferromagnetic for (anti)ferromagnetic Kitaev interactions. However, when two layers have opposite sign of the Kitaev interaction, we observe a notable weakening of magnetic ordering tendencies and the Kitaev spin liquid survives up to a remarkably larger interlayer exchange. Our mean-field analysis suggests the emergence of an intermediate gapped $\mathbb{Z}_2$ spin liquid state, which eventually becomes unstable upon vison condensation. The confined phase is described by a highly frustrated $120^\circ$ compass model. We furthermore use perturbation theory to study the model with the Ising axis pointing along $\hat{z}$-axis or lying in the $xy$-plane. In both cases, our analysis reveals the formation of 1D Ising chains, which remain decoupled in perturbation theory, resulting in a subextensive ground-state degeneracy. Our results highlight the interplay between topological order and magnetic ordering tendencies in bilayer quantum spin liquids.