核多体问题的预处理：重要性截断与张量因式分解技术
Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
摘要：
核A体问题的解决受到多体算子规模的严重限制。这些限制通常与相关张量的（迭代）存储以及与在计算各种感兴趣的量时与其多次收缩相关的计算时间有关。然而，并不是所有的自由度封装到这些张量同样有助于多体观测的描述。识别系统和主导模式，一个相关的目标是实现一个\emph{a priori}减少到最相关的自由度，通过预处理的A体问题。本文件致力于分析两种不同的范式这样做。张量的因式分解的低秩的，其诀窍最近已转移到领域的原子核结构，相比减少张量的指数大小的基础上的重要性截断。虽然我们的目标是最终利用这些预处理工具的背景下，非微扰多体方法，基准计算目前进行的框架内的微扰理论。更具体地说，我们采用最近推出的Bogoliubov多体微扰理论，系统地适用于开壳层原子核显示强相关性。这种扩展的微扰理论作为一个跳跃的开始，非微扰Bogoliubov耦合集群和Gorkov自洽格林函数理论。在“小”模型空间中获得的结果同样令人鼓舞的张量分解和重要性截断技术。虽然前者需要显着的数值发展应用于大型模型空间，后者目前应用于这方面，并表现出巨大的潜力，使高精度的计算，大大降低了计算成本。
英文摘要：
The solution of the nuclear A-body problem encounters severe limitations from the size of many-body operators. These limitations are typically related to both the (iterative) storing of the associated tensors and to the computational time related to their multiple contractions in the calculation of various quantities of interest. However, not all the degrees of freedom encapsulated into these tensors equally contribute to the description of many-body observables. Identifying systematic and dominating patterns, a relevant objective is to achieve an \emph{a priori} reduction to the most relevant degrees of freedom via a pre-processing of the A-body problem. The present paper is dedicated to the analysis of two different paradigms to do so. The factorization of tensors in terms of lower-rank ones, whose know-how has been recently transferred to the realm of nuclear structure, is compared to a reduction of the tensors' index size based on an importance truncation. While the objective is to eventually utilize these pre-processing tools in the context of non-perturbative many-body methods, benchmark calculations are presently performed within the frame of perturbation theory. More specifically, we employ the recently introduced Bogoliubov many-body perturbation theory that is systematically applicable to open-shell nuclei displaying strong correlations. This extended perturbation theory serves as a jumpstart for non-perturbative Bogoliubov coupled cluster and Gorkov self-consistent Green's function theories. Results obtained in "small" model spaces are equally encouraging for tensor factorization and importance truncation techniques. While the former requires significant numerical developments to be applied in large model spaces, the latter is presently applied in this context and demonstrates great potential to enable high-accuracy calculations at a much reduced computational cost.
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