On Construction of Projection Operators.
On Construction of Projection Operators.
复制标题
论投影算子的构建。
DOI：
10.1021/acs.jpca.9b01103
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
A. Izmaylov
中科院分区：
文献类型：
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作者：
A. Izmaylov
考虑了对称算子特征子空间上投影算子的构造问题。这个问题出现在许多求解与时间无关和与时间相关的量子问题的近似方法中，并且其解决方案确保了近似方法的发展中适当的物理对称性。投影仪形式被寻求为对称算子及其表征感兴趣的本征子空间的本征值的函数。这种形式通过两个步骤获得：(1) 识别一组对称算子（例如群和李代数）内的代数结构，以及 (2) 构造各个对称算子的投影算子。第一步对于高效的投影算子构造至关重要，因为它允许使用有关当前代数结构的不可约表示的信息。所讨论的方法有可能刺激强相关系统电子结构和量子计算中变分方法的进一步发展。
The problem of construction of projection operators on eigensubspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution ensures proper physical symmetries in development of approximate methods. The projector form is sought as a function of symmetry operators and their eigenvalues characterizing the eigensubspace of interest. This form is obtained in two steps: (1) identification of algebraic structures within a set of symmetry operators (e.g., groups and Lie algebras) and (2) construction of the projection operators for individual symmetry operators. The first step is crucial for efficient projection operator construction because it allows for use of information on irreducible representations of the present algebraic structure. The discussed approaches have potential to stimulate further developments of variational approaches for electronic structure of strongly correlated systems and in quantum computing.