ADG：多体图III的自动生成和评估。Bogoliubov介质内相似重整化群形式
ADG: Automated generation and evaluation of many-body diagrams III. Bogoliubov in-medium similarity renormalization group formalism
摘要：
本文件有两个目标。首先，提出了一种新的适用于超流开壳层核的展开多体方法，即Bogoliubov介质内相似重整化群（BIMSRG）理论。标准的单参考IMSRG理论的这种推广的封闭壳层系统的耦合集群，自洽格林函数或多体微扰理论的最近扩展平行。在IMSRG理论的领域内，BIMSRG提供了一个有趣的替代已经存在的多参考IMSRG（MR-IMSRG）方法适用于开壳层核。低阶近似的代数方程，即，BIMSRG（1）和BIMSRG（2）可以很容易地手工导出。然而，这样的方法对于BIMSRG（3）方程的推导来说已经变得不切实际并且容易出错，而BIMSRG（3）方程最终需要达到高精度。基于BIMSRG理论的图解公式，本文的第二个目标是描述ADG代码的第三个版本（v3.0.0），该代码自动（1）生成所有有效的BIMSRG（n）图，（2）在几秒钟内计算其代数表达式。这是在这样一种方式，方程可以很容易地检索到的流动方程和BIMSRG的马格努斯展开配方。在这项工作的基础上，未来的第一个目标是数值实现BIMSRG（2）（最终BIMSRG（3））方程，并对中等质量开壳层核进行从头计算。
英文摘要：
The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green's function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0.0) of the ADG code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei.
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