arXiv 1607.015282016-07quant-ph

多电子Dirac-Coulomb哈密顿量的新量子数

New quantum number for the many-electron Dirac-Coulomb Hamiltonian

Stanislav Komorovsky, Michal Repisky, Lukáš Bučinský

备注：: 15 pages, published in Phys. Rev. A, one FORTRAN program; Changes: minor text formatting, add supplemental material as Appendix I, add comparison with three open-shell electrons to Sec. VII last paragraph
发表信息：: Phys. Rev. A, 94 (2016) 052104
DOI：: 10.1103/PhysRevA.94.052104

摘要：

由于在相对论领域打破了自旋对称性，物理科学中一个强大的工具就失去了。在这项工作中，我们研究了一种替代的自旋对称性的系统描述的多电子狄拉克-库仑哈密顿。我们证明了多电子算符的平方$\mathcal{K}_+$是一个线性厄米算符，它与有限Fock子空间中的Dirac-Coulomb哈密顿量交换.与标准幺正多电子TR算符$\mathcal{K}$的平方相反，$\mathcal{K}^2_+$具有丰富的本征谱，有可能取代相对论域中的自旋对称性。我们证明，$\mathcal{K}_+$是连接到$\mathcal{K}$通过指数映射，以相同的方式自旋算子映射到自旋旋转群。因此，我们称$\mathcal{K}_+$为多电子TR对称性的生成元。通过在Kramers限制的Slater行列式的基础上对角化算符$\mathcal{K}^2_+$，我们引入了组态态函数的相对论变体，记作Kramers CSF.与$\mathcal{K}^2_+$相关的一个新的量子数在许多领域有潜在的应用，例如：（a）设计有效的自旋哈密顿量，用于含重元素体系的电子自旋共振谱，（b）提高相对论计算化学和物理中多电子问题的求解效率，（c）计算量子数的计算方法。（c）在非限制密度泛函中定义Kramers污染，Hartree-Fock理论是非相对论域中自旋污染的相对论模拟。

英文摘要：

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator $\mathcal{K}_+$, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator $\mathcal{K}$, the $\mathcal{K}^2_+$ has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that $\mathcal{K}_+$ is connected to $\mathcal{K}$ through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call $\mathcal{K}_+$ the generator of the many-electron TR symmetry. By diagonalizing the operator $\mathcal{K}^2_+$ in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with $\mathcal{K}^2_+$ has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree--Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain.

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