Irreducible tensor operator techniques and point-group symmetries for molecular magnetism

对于足够小的自旋系统，哈密顿量的数值精确和完全对角化是评估和讨论所有静态、动态和热力学性质的最终选择方法，例如磁性分子。然而，由于底层希尔伯特空间的巨大维度，这样的计算往往受到严格的限制。在最近发展了使用完全自旋-旋转，即SU(2)对称性和一般点群对称性的精确对角化方法[1]之后，我们瞄准了这个项目的三个主要目标。首先，我们希望与我们的化学伙伴合作，研究最新的分子化合物的磁性。其次，我们计划进一步发展一种方案，通过结合转动带的思想和对称性论证来近似获得大量的低能级本征值。第三，我们希望在两个方面改进和进一步发展数值程序：公开它和开发一个能够处理更大自旋系统的高级版本。该项目最好由罗曼·施纳尔负责，他在博士期间开发了这一方法。

For small enough spin systems numerical exact and complete diagonalization of the Hamiltonian is the ultimate method of choice to evaluate and discuss all static, dynamic, and thermodynamic properties, e.g. of magnetic molecules. Nevertheless, such calculations are very often severely restricted due to the huge dimension of the underlying Hilbert space. After having recently developed exact diagonalization methods using the full spin-rotational, i.e. SU(2), symmetry together with general point-group symmetries [1] we aim at three major objectives in this project. Firstly, we would like to investigate very recent molecular compounds for their magnetic properties in collaboration with our chemical partners. Secondly, we plan to further develop a scheme to approximately obtain a large number of low-lying energy eigenvalues by combining the idea of rotational bands as well as symmetry arguments. Thirdly, we want to improve and further develop the numerical program in two aspects: it shall be made public and an advanced version that is capable to treat even larger spin systems shall be developed. Preferably, the project should be carried out by Roman Schnalle, who developed the method in his Ph. D.