各向异性库仑相互作用的多极表示
Multipole representation for anisotropic Coulomb interactions
摘要：
提出了固体中各向异性库仑相互作用的多极表示。任何局部相互作用都可以表示为两个多极算符的乘积，并根据点群对称性对相互作用参数进行了系统的分类。多极相互作用的形式不仅受对称性和厄米性的制约，而且还受相互作用空间结构的制约，空间结构与奇秩多极相互作用的有无密切相关。作为一个示范性的演示，SrVO $_3$的屏蔽库仑相互作用被认为是，只有几个参数是必要的，其描述。通过与未屏蔽的版本进行比较，发现完全对称的$A_1$表示被强烈抑制，但$A_1$分量仍然对相互作用的各向异性部分做出了主要贡献。各向异性相互作用也适用于本地化的两个$f$ -电子波函数，它给出了相同的顺序的贡献作为一个体能级分裂估计的能带结构计算。
英文摘要：
Multipole representation is proposed for the anisotropic Coulomb interactions in solids. Any local interactions can be expressed as the product of two multipole operators, and the interaction parameters are systematically classified based on the point group symmetry. The form of the multipole interactions are restricted not only by the symmetry and Hermiticity but also by the spatial structure of the interaction, which is closely related to the presence or absence of the odd-rank multipoles. As an exemplary demonstration, the screened Coulomb interaction for SrVO$_3$ is considered, where only a few parameters are necessary for its description. By comparing it with the unscreened version, the totally symmetric $A_1$ representation is found to be strongly suppressed, but the $A_1$ component still gives a dominant contribution for the anisotropic part of the interaction. The anisotropic interactions are also applied to the localized two $f$-electron wave functions, which give the same-order contribution as the one-body level splitting estimated by the band structure calculation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
