计算磁性分子的能谱：实空间和自旋空间对称性的应用
Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
摘要：
确定小自旋系统的能谱，例如磁性分子的能谱，是一个要求很高的数值问题。在这项工作中，我们回顾数值方法对角化海森堡哈密顿量，采用对称性，特别是我们专注于自旋旋转对称性SU（2）与点群对称性相结合。利用这些方法，人们能够将哈密顿量块对角化，从而处理前所未有大小的自旋系统。此外，它还提供了一个光谱标记的不可约表示，这是有帮助的，当解释跃迁诱导的电子顺磁共振（EPR），核磁共振（NMR）或非弹性中子散射（INS）。我们的目标是为读者提供如何建立这样一个对角化方案的详细知识。
英文摘要：
The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.
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