Modular Tensor Diagram Approach for the Construction of Spin Eigenfunctions: The Case Study of Exciton Pair States.,The Journal of Physical Chemistry A

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Modular Tensor Diagram Approach for the Construction of Spin Eigenfunctions: The Case Study of Exciton Pair States.
The Journal of Physical Chemistry A ( IF 2.7 ) Pub Date : 2020-06-18 , DOI: 10.1021/acs.jpca.0c00263
Guohua Tao _{1,

2} , Yunshu Tan _{1,

2}

Affiliation

Mapping out the high-dimensional state space would be valuable for better understanding the multistate quantum systems. Here, we demonstrate that high-dimensional spin state space can be mapped onto a tensor diagram in full dimension or self-similarly onto the reduced base state space. Based on the tensor diagram, a modular approach is proposed to construct spin eigenfunctions taking the basis of the lower-dimensional space as modules. The implementation of the approach on exciton pair states results in 16 spin eigenstates including 2 singlet states, 3 triplet states, and 1 quintet state with proper symmetry, in contrast to the ones generated using the conventional branching diagram method. The corresponding state energies obtained show the order of spin eigenstates reverses with respect to spin multiplicity. Interestingly, the state space can be decomposed into three subspaces corresponding to the singlet–singlet pair, singlet–triplet pair, and triplet–triplet pair, resulting in a modular structure that is invariant as intermolecular interactions diminish. The proposed approach offers a new perspective on the state space structure of multiple spin states, featuring a hierarchical symmetry, which could be extended to general high-dimensional quantum multistate systems.

中文翻译：

自旋本征函数构建的模块化张量图方法：激子对状态的案例研究。

绘制高维状态空间对于更好地理解多态量子系统将是有价值的。在这里，我们证明了高维自旋状态空间可以全尺寸映射到张量图上，也可以自相似地映射到简化的基态空间上。基于张量图，提出了一种模块化方法，以低维空间为模块构造自旋本征函数。该方法在激子对状态上的实现导致16个自旋本征状态，包括2个单重态，3个三重态和1个五重态，具有适当的对称性，这与使用常规分支图方法生成的状态相反。所获得的相应状态能量显示了自旋本征态相对于自旋多重性反转的顺序。有趣的是状态空间可以分解为三个子空间，分别对应于单重态-单重态对，单重态-三重态对和三重态-三重态对，从而使模块结构随着分子间相互作用的减少而不变。所提出的方法为具有多重对称性的多重自旋态的状态空间结构提供了新的视角，可以扩展到一般的高维量子多态系统。

更新日期：2020-07-02

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