基于规范多元分解的分子电子哈密顿量的紧凑积和形式
Compact sum-of-products form of the molecular electronic Hamiltonian based on canonical polyadic decomposition
AI总结：
本文提出基于规范多元分解将二次量子化电子哈密顿量表示为紧凑积和形式，并通过交替最小二乘实现最优紧凑化，在激发态水分子、反式多烯和甘氨酸电荷迁移等体系中验证了方法的有效性。
摘要：
我们提出了一种将二次量子化电子哈密顿量表示为紧凑积和（SOP）形式的方法。该方法基于将原始哈密顿量投影到由自旋轨道群构成的子Fock空间上，并进行规范多元分解（CPD）。获得规范多元形式的算法从一个精确的积和出发，然后利用交替最小二乘程序对其进行最优紧凑化。我们讨论了这种特定SOP与相关形式的关系，即Tucker格式和通常与矩阵乘积态结合使用的矩阵乘积算符。我们在激发态水分子的电子动力学、反式多烯以及内价电离后甘氨酸中的电荷迁移上对该方法进行了基准测试。量子动力学采用二次量子化表示下的多层多组态时间相关Hartree方法（MCTDH-SQR）进行。其他基于树张量Ansätze的方法也可能从这一通用方法中受益。
英文摘要：
We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sum-of-products (SOP) form. The approach is based on the canonical polyadic decomposition (CPD) of the original Hamiltonian projected onto the sub-Fock spaces formed by groups of spin orbitals. The algorithm for obtaining the canonical polyadic form starts from an exact sum-of-products, which is then optimally compactified using an alternating least-squares procedure. We discuss the relation of this specific SOP with related forms, namely the Tucker format and the matrix product operator often used in conjunction with matrix product states. We benchmark the method on the electronic dynamics of an excited water molecule, trans-polyenes, and the charge migration in glycine upon inner-valence ionization. The quantum dynamics are performed with the multilayer multi-configuration time-dependent Hartree method in second quantization representation (MCTDH-SQR). Other methods based on tree-tensor Ansätze may profit from this general approach.
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