The spin structure of wave functions is reflected in the magnetic structure of the one-particle density matrix. Indeed, for single determinants we can use either one to determine the other. In this work we discuss how one can simply examine the one-particle density matrix to faithfully determine whether the spin magnetization density vector field is collinear, coplanar, or noncoplanar. For single determinants, this test suffices to distinguish collinear determinants which are eigenfunctions of Ŝ_n̂ from noncollinear determinants which are not. We also point out the close relationship between noncoplanar magnetism on the one hand and complex conjugation symmetry breaking on the other. Finally, we use these ideas to classify the various ways single determinant wave functions break and respect symmetries of the Hamiltonian in terms of their one-particle density matrix.

中文翻译：

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密度矩阵的磁性结构

波函数的自旋结构反映在单粒子密度矩阵的磁结构中。确实，对于单个行列式，我们可以使用其中一个来确定另一个。在这项工作中，我们讨论了如何可以简单地检查一个粒子密度矩阵，以忠实地确定自旋磁化强度矢量场是共线的，共面的还是非共面的。对于单决定簇，这种测试足以区分线的决定它们是本征函数的小号_Ñ从非共线行列式中得出。我们还指出，一方面非共面磁性与另一方面破坏复杂的共轭对称性之间的密切关系。最后，我们使用这些思想对单行列式波动函数破坏和尊重哈密顿量的单粒子密度矩阵的对称性的各种方式进行分类。