论文标题
Kagome $ j_ {1} -j_ {3} $ Heisenberg模型中竞争的紧急potts订单和可能的nematic旋转液体
Competing emergent Potts orders and possible nematic spin liquids in the Kagome $J_{1}-J_{3}$ Heisenberg model
论文作者
论文摘要
kagome抗fiferromagnet的极端挫败感使在经典水平或量子水平上实现大量紧密竞争的磁相成为可能。受到kagome抗fiferromagnet vesignieite bacu $ _ {3} $ v $ _ {2} $ o $ $ $ _ {8} $（oh）$ _ {2} $的动机在Kagome晶格（KAFHM）上定义的模型。虽然先前表明，第三次旋转之间的大型抗铁磁交换可以通过逐项订购的机制来推动出现的$ q = 4 $ potts订单，但在所谓的“灰色区域”中，Luttinger-Tisza标准无法预测经典的订购模式，这是难以捉摸的。通过广泛的蒙特卡洛模拟，我们发现“灰色区域”的特征是竞争的紧急$ q = 3 $和$ q = 4 $ potts订单，其出现的出现超出了对常规订购序列机制的描述。我们的schwinger玻色子在“灰色区域”中的平均场计算确认了potts-3顺序的存在，处于量子$ j_ {1} -j_ {3} $ kafhm的基础状态。发现预测的potts-3状态采用两种不同的形式，这些形式以其投射对称组特征（PSG或量子顺序）区分，尽管它们具有完全相同的对称性。与精确的对角线化的比较结果在一个36个地点簇上结果表明，“灰色区域”确实可以携带列型旋转液态基态，该状态具有各向异性环结构，周围是$ \ mathbf {q} = 0 $ point spinon分散关系。我们发现，这种极度沮丧磁铁的“灰色区域”应该更好地作为操场，以研究异国情调的新兴阶段之间的丰富竞争，而不是对其理论分析的负担。
The extreme frustration in the Kagome antiferromagnet makes it possible to realize a large number of closely competing magnetic phases either at the classical or the quantum level. Motivated by recent neutron scattering study on the Kagome antiferromagnet vesignieite BaCu$_{3}$V$_{2}$O$_{8}$(OH)$_{2}$, we have made systematic investigation of the phase diagram of the classical and quantum $J_{1}-J_{3}$ antiferromagnetic Heisenberg model defined on the Kagome lattice(KAFHM). While it is shown previously that a large antiferromagnetic exchange between the third-neighboring spins can drive an emergent $q=4$ Potts order through the order-by-disorder mechanism, it is elusive what will happen in the so called "grey region" where the Luttinger-Tisza criteria fails to predict the classical ordering pattern. Through extensive Monte Carlo simulation, we find that the "grey region" is characterized by competing emergent $q=3$ and $q=4$ Potts order, whose emergence are beyond the description of the conventional order-by-disorder mechanism. Our Schwinger Boson mean field calculation in the "grey region" confirms the existence of the Potts-3 order in the ground state of quantum $J_{1}-J_{3}$ KAFHM. The predicted Potts-3 state is found to take two different forms distinguished by their projective symmetry group character(PSG or quantum order), although they have exactly the same symmetry. A comparison with the exact diagonalization result on a 36-site cluster shows that the "grey region" may indeed host a nematic spin liquid ground state featuring an anisotropic ring structure around the $\mathbf{q}=0$ point in its spinon dispersion relation. We find that such "grey region" of extremely frustrated magnets should better be taken as the playground to study the rich competition between exotic emergent phases, rather than a burden on their theoretical analysis.
