论文标题
三角形$ j $ - $ k $ - $γ$模型中全球相图的全面研究
Comprehensive study of the global phase diagram in the triangular $J$-$K$-$Γ$ model
论文作者
论文摘要
著名的Kitaev Honeycomb模型提供了一个具有分析性的示例，具有精确的量子自旋液态基态。在实际材料中，还有其他类型的互动，除了Kitaev耦合（$ K $），例如Heisenberg（$ j $）和对称的偏高（$γ$）项，这些交互也可以推广到三角形晶格。在这里，我们使用确切的对角线化，经典的蒙特卡洛和分析方法的组合，对覆盖完整参数区域的三角形晶格的$ j $ - $ k $ - $γ$模型进行了全面研究。在香港极限（$γ= 0 $）中，我们发现五个量子相与它们的经典同行非常相似。其中，Stripe-A和双Néel阶段对$γ$项非常强大，尤其是Stripe-A延伸到连接$ K = -1 $的区域，$ K = 1 $，对于$γ<0 $。尽管120美元$^\ Circ $néel阶段也扩展到有限的$γ$，但与以前的经典结果相比，其区域大大减少了。有趣的是，对于无限的$γ$相互作用，铁磁（称为FM-A）相位和条纹-B相不稳定。此外，我们找到了$γ\ ne 0 $的五个新阶段，这些阶段是由量子和经典数值方法详细阐述的。在古典研究中，先前确定为120 $^\ circ $néel阶段的空间的一部分被发现使位于调制条纹阶段。根据$γ$的迹象，FM-A相转移到FM-B（$γ> 0 $）和FM-C（$γ<0 $）相具有不同的旋转方向的相位，以及Stripe-B相转移到Stripe-C（$γ> 0 $）和Stripe-A（$γ<0 $）中。由于Heisenberg，KiateV和$γ$相互作用的相互作用，在正$γ$点附近，我们发现可能具有旋转激发的连续体的量子自旋液体。
The celebrated Kitaev honeycomb model provides an analytically tractable example with an exact quantum spin liquid ground state. While in real materials, other types of interactions besides the Kitaev coupling ($K$) are present, such as the Heisenberg ($J$) and symmetric off-diagonal ($Γ$) terms, and these interactions can also be generalized to a triangular lattice. Here, we carry out a comprehensive study of the $J$-$K$-$Γ$ model on the triangular lattice covering the full parameters region, using the combination of the exact diagonalization, classical Monte Carlo and analytic methods. In the HK limit ($Γ=0$), we find five quantum phases which are quite similar to their classical counterparts. Among them, the stripe-A and dual Néel phase are robust against the $Γ$ term, in particular the stripe-A extends to the region connecting the $K=-1$ and $K=1$ for $Γ<0$. Though the 120$^\circ$ Néel phase also extends to a finite $Γ$, its region has been largely reduced compared to the previous classical result. Interestingly, the ferromagnetic (dubbed as FM-A) phase and the stripe-B phase are unstable in response to an infinitesimal $Γ$ interaction. Moreover, we find five new phases for $Γ\ne 0$ which are elaborated by both the quantum and classical numerical methods. Part of the space previously identified as 120$^\circ$ Néel phase in the classical study is found to give way to the modulated stripe phase. Depending on the sign of the $Γ$, the FM-A phase transits into the FM-B ($Γ>0$) and FM-C ($Γ<0$) phase with different spin orientations, and the stripe-B phase transits into the stripe-C ($Γ>0$) and stripe-A ($Γ<0$). Around the positive $Γ$ point, due to the interplay of the Heisenberg, Kiatev and $Γ$ interactions, we find a possible quantum spin liquid with a continuum in spin excitations.
