Finite-temperature phase transition to a quantum spin liquid in a three-dimensional Kitaev model on a hyperhoneycomb lattice
Finite-temperature phase transition to a quantum spin liquid in a three-dimensional Kitaev model on a hyperhoneycomb lattice
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DOI：
10.1103/physrevb.89.115125
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发表时间：
2013-09
影响因子：
3.7
通讯作者：
J. Nasu;T. Kaji;K. Matsuura;M. Udagawa;Y. Motome
中科院分区：
文献类型：
--
作者：
J. Nasu;T. Kaji;K. Matsuura;M. Udagawa;Y. Motome
我们提出了数值证据的存在下的有限温度（$T$）相变分离顺磁体和量子自旋液体在一个三维的Kitaev模型定义在一个超蜂窝晶格的极限强各向异性的三维变体;该模型被映射到一个有效的伊辛型模型，其中基本的激发包括翻转伊辛型变量的闭环。通过MonteCarlo模拟分析这个有效模型，我们发现在有限的临界温度T_c下存在从量子自旋液体到顺磁体的相变。我们还计算了原始量子自旋的磁性。我们发现磁化率在T_c以上有一个很宽的峰，在高T_c时服从居里定律，在低T_c时接近一个非零的货车Vleck型常数。虽然磁化率在T_c处连续变化，但其T_c导数在T_c处出现临界发散。我们还澄清，动力学自旋相关函数是动量无关的，但显示对应于离散激发的量子化峰。虽然相变伴随着没有明显的对称性破缺的伊辛型变量以及原始的量子自旋，我们从拓扑的观点来描述它。我们发现，通过定义的伊辛型变量的回路的磁通密度，过渡被解释为发生从零通量量子自旋液体的非零通量顺磁体;后者具有库仑性质，由于当地的限制。的伊辛型变量的全局约束的作用进行检查，在二维循环模型中的结果进行比较。本文还讨论了我们的模型与金刚石晶格上的伊辛模型的对应关系。最近发现的超蜂窝化合物，$\beta$-Li$_2$IrO$_3$，我们的研究结果的一个可能的相关性被提及。
We present numerical evidence for the presence of a finite-temperature ($T$) phase transition separating paramagnet and quantum spin liquid in a three-dimensional variant of the Kitaev model defined on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from quantum spin liquid to paramagnet at a finite critical temperature $T_c$. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above $T_c$, while it obeys the Curie law at high $T$ and approaches a nonzero Van Vleck-type constant at low $T$. Although the susceptibility changes continuously at $T_c$, its $T$ derivative shows critical divergence at $T_c$. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to the discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables as well as the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Ising-type variables, the transition is interpreted as the one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. A correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently-discovered hyperhoneycomb compound, $\beta$-Li$_2$IrO$_3$, is mentioned.