AI 中文总结
研究单格点密度矩阵的多极子分解，通过扩展公式构建完备正交基，按对称性分类多极子，可唯一识别密度矩阵多极矩，还通过计算电环形单极矩分析手性三角碲对映体。
AI 中文摘要
单格点密度矩阵的多极子分解提供了局部电子自由度的对称适配表示。传统的所谓固定壳层公式不能涵盖整个局部单粒子算符空间，因为仅解析了在同一轨道\(l\)内映射的算符。在此，我们通过将现有公式扩展到壳层间算符，构建了用于局部密度矩阵的实厄米多极子算符的完备正交基。我们通过首先分解轨道和自旋算符空间，将多极子分解重新审视为由\(\mathrm{SO}(3)\)进行的算符空间分解。然后通过耦合它们得到自旋\(\frac{1}{2}\)局部单粒子算符空间，与现有固定壳层公式保持一致。接着我们按宇称和时间反演对称性对多极子进行分类，这使得能够唯一识别对完全对称解析可观测量的期望值有贡献的密度矩阵的多极矩。作为应用，我们通过计算由对称性选择的电环形单极矩来分析手性三角碲的两种对映体。
英文摘要
The multipole decomposition of the single-site density matrix provides a symmetry-adapted representation of local electronic degrees of freedom. Conventional, so-called fixed-shell, formulations do not span the full local single-particle operator space, as only operators mapping within the same orbital $l$ are resolved. Here we construct a complete orthogonal basis of real Hermitian multipole operators for the local density matrix by extending the existing formulation to inter-shell operators. We revisit the multipole decomposition as a decomposition of the operator space by $\mathrm{SO}(3)$ by first decomposing the orbital and spin operator spaces. Then by coupling them we arrive at the spin-$\frac{1}{2}$ local single-particle operator space, staying consistent with the existing fixed-shell formulations. We then classify the multipoles by parity and time-reversal symmetry, which allows for unique identification of multipole moments of the density matrix that contribute to expectation values of fully symmetry-resolved observables. As an application, we analyze the two enantiomers of chiral trigonal tellurium by computing the electric toroidal monopole moment selected by symmetry.
Comments18 pages, 1 figure
