强关联体系下单参考基态的树张量网络叠加
Superpositions of tree-tensor networks for single-reference ground states in the strong correlation regime
AI总结：
本文提出树张量网络叠加（STTN）方法，通过低秩张量分解表示簇算符，将单参考耦合簇方法扩展至强关联体系，在二维Hubbard团簇中验证了其紧凑性与高精度。
摘要：
强关联体系下的费米子多体问题非常难以处理。在之前的工作（Phys. Rev. B 101, 045109 (2020)）中，我们提出利用低秩张量分解（LRTD）表示簇算符，将单参考耦合簇（SRCC）方法扩展到强关联体系，且不按激发数量进行截断。为此，我们提出了一种称为“树张量网络叠加”（STTN）的新型LRTD，它使用相同的构建块来定义CC方程中涉及的所有张量，并在给定张量的分解中结合不同的“通道”，即激发粒子与空穴之间不同类型的配对。这两个原则旨在全局最小化精确表示基态所需的自由参数总数。在本工作中，我们通过使用STTN来表达CC簇算符振幅和波函数系数，证明了STTN确实可以成为强关联基态的紧凑且精确的表示，这些系数对应于半填充下小型二维Hubbard团簇的精确基态，最高包含三粒子-空穴激发。我们通过使用比CCSD近似中方程数量更少的自由参数，即远小于拟合张量元素数量的参数，展示了STTN的紧凑性。我们发现，对于所考虑的系统，随着系统尺寸的增加，STTN变得更加精确，并且在最强关联张量的分解中结合不同通道对于获得良好的精度至关重要。
英文摘要：
The fermionic many-body problem in the strong correlation regime is notoriously difficult to tackle. In a previous work (Phys. Rev. B 101, 045109 (2020)), we have proposed to extend the single-reference coupled-cluster (SRCC) method to the strong correlation regime using low-rank tensor decompositions (LRTD) to express the cluster operator, without truncating it with respect to the number of excitations. For that purpose, we have proposed a new type of LRTD called ``superpositions of tree-tensor networks'' (STTN), which use the same set of building blocs to define all the tensors involved in the CC equations, and combine different ``channels'', i.e. different types of pairing among excited particles and holes, in the decomposition of a given tensor. Those two principles are aimed at globally minimizing the total number of free parameters required to accurately represent the ground state. In this work, we show that STTN can indeed be compact and accurate representations of strongly correlated ground states by using them to express the CC cluster operator amplitudes and wave function coefficients of exact grounds states of small two-dimensional Hubbard clusters, at half-filling, up to three particle-hole excitations. We show the compactness of STTN by using a number of free parameters smaller than the number of equations in the CCSD approximation, i.e. much smaller than the number of fitted tensor elements. We find that, for the systems considered, the STTN are more accurate as the size of the system increases and that combining different channels in the decompositions of the most strongly correlated tensors is crucial to obtain good accuracy.
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