基于射影对称群分析的星形晶格反铁磁体量子相位分类
Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis
摘要：
我们研究了星型晶格上海森堡反铁磁体的可能量子基态，它可能在最近发现的聚合醋酸铁Fe $_3$（$μ_3$ -O）（$μ$ -OAc）$_6$（H $_2$ O）$_3$ [Fe $_3$（$μ_3$ -O）（$μ$ -OAc）$_{7.5}$ ] $_2\cdot$ 7 H $_2$ O中实现.尽管这种材料中的Fe $^{\rm III}$磁矩携带自旋5/2，并且系统最终在低温下磁性有序，但磁有序温度远低于估计的居里-外斯温度，揭示了自旋相互作用的受抑性质。预计这种材料的低自旋类似物可能会在未来合成，我们调查的影响，量子涨落的星形晶格反铁磁体使用大- $N$ Sp（$N$）平均场理论和投影对称群分析可能的玻色子量子自旋液相。结果表明，当最近邻价键振幅不为零时，只存在两个带隙的$Z_2$自旋液相。特别地，在最近邻交换模型中具有较低能量的自旋液相可以对于相对较高的自旋幅度而稳定。因此，它可能是实现量子自旋液态的一个更好的候选者。我们还确定了由玻色子自旋子在两个不同的自旋液相中的凝聚所产生的磁有序图案。我们预计这些磁有序模式将直接相关的低温有序相的醋酸铁。包含所有这些阶段和各种二聚状态的相图获得的最近邻交换模型和它的影响进行了讨论。
英文摘要：
We study possible quantum ground states of the Heisenberg antiferromagnet on the star lattice, which may be realized in the recently discovered polymeric Iron Acetate, Fe$_3$($μ_3$-O)($μ$-OAc)$_6$(H$_2$O)$_3$[Fe$_3$($μ_3$-O)($μ$-OAc)$_{7.5}$]$_2\cdot$ 7H$_2$O. Even though the Fe$^{\rm III}$ moment in this material carries spin-5/2 and the system eventually orders magnetically at low temperatures, the magnetic ordering temperature is much lower than the estimated Curie-Weiss temperature, revealing the frustrated nature of the spin interactions. Anticipating that a lower spin analog of this material may be synthesized in future, we investigate the effect of quantum fluctuations on the star-lattice antiferromagnet using a large-$N$ Sp($N$) mean field theory and a projective symmetry group analysis for possible bosonic quantum spin liquid phases. It is found that there exist only two distinct gapped $Z_2$ spin liquid phases with bosonic spinons for non-vanishing nearest-neighbor valence-bond-amplitudes. In particular, the spin liquid phase which has a lower energy in the nearest-neighbor exchange model can be stabilized for relatively higher spin magnitudes. Hence it is perhaps a better candidate for the realization of quantum spin liquid state. We also determine the magnetic ordering patterns resulting from the condensation of the bosonic spinons in the two different spin liquid phases. We expect these magnetic ordering patterns would directly be relevant for the low temperature ordered phase of the Iron Acetate. The phase diagram containing all of these phases and various dimerized states are obtained for the nearest-neighbor exchange model and its implications are discussed.
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