具有60个量子自旋的帽状kagome分子的磁性
Magnetic properties of a capped kagome molecule with 60 quantum spins
摘要：
我们计算基态的各向同性，反铁磁海森堡模型的方钠石笼几何性质。这是一个60自旋的球形分子，具有24个顶点共享四面体，可以被认为是一个加帽的kagome晶格的分子模拟物，并且已经用高自旋稀土原子合成。在这里，我们专注于$S=1/2$的情况下，量子效应是最强的。我们采用SU（2）对称密度矩阵重整化群（DMRG）。我们发现一个三重简并的基态，打破了空间对称性，并分裂成三个大的部分，几乎是相互去耦的分子。这与大多数已知的球形分子的行为形成鲜明对比。在方法层面上，断开导致DMRG内的“玻璃态动力学”，无法通过标准技术进行定位。在有限磁场的存在下，我们发现在饱和度的4/5、3/5和1/5处有宽的磁化平台，这可以理解为局域化的磁振子、单重态和双重态，它们又几乎彼此解耦。在饱和场中，零点熵是以玻耳兹曼常量为单位的$S=\ln(182)\approx 5.2$。
英文摘要：
We compute ground-state properties of the isotropic, antiferromagnetic Heisenberg model on the sodalite cage geometry. This is a 60-spin spherical molecule with 24 vertex-sharing tetrahedra which can be regarded as a molecular analogue of a capped kagome lattice and which has been synthesized with high-spin rare-earth atoms. Here, we focus on the $S=1/2$ case where quantum effects are strongest. We employ the SU(2)-symmetric density-matrix renormalization group (DMRG). We find a threefold degenerate ground state that breaks the spatial symmetry and that splits up the molecule into three large parts which are almost decoupled from each other. This stands in sharp contrast to the behaviour of most known spherical molecules. On a methodological level, the disconnection leads to "glassy dynamics" within the DMRG that cannot be targeted via standard techniques. In the presence of finite magnetic fields, we find broad magnetization plateaus at 4/5, 3/5, and 1/5 of the saturation, which one can understand in terms of localized magnons, singlets, and doublets which are again nearly decoupled from each other. At the saturation field, the zero-point entropy is $S=\ln(182)\approx 5.2$ in units of the Boltzmann constant.
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