Abstract We describe the second version (v2.0.0) of the code ADG that automatically (1) generates all valid off-diagonal Bogoliubov many-body perturbation theory diagrams at play in particle-number projected Bogoliubov many-body perturbation theory (PNP-BMBPT) and (2) evaluates their algebraic expression to be implemented for numerical applications. This is achieved at any perturbative order p for a Hamiltonian containing both two-body (four-legs) and three-body (six-legs) interactions (vertices). All valid off-diagonal BMBPT diagrams of order p are systematically generated from the set of diagonal, i.e.,unprojected, BMBPT diagrams. The production of the latter were described at length in Arthuis et al. (2019) dealing with the first version of ADG . The automated evaluation of off-diagonal BMBPT diagrams relies both on the application of algebraic Feynman’s rules and on the identification of a powerful diagrammatic rule providing the result of the remaining p -tuple time integral. The new diagrammatic rule generalizes the one already identified in Arthuis et al. (2019) to evaluate diagonal BMBPT diagrams independently of their perturbative order and topology. The code ADG is written in Python3 and uses the graph manipulation package NetworkX. The code is kept flexible enough to be further expanded throughout the years to tackle the diagrammatics at play in various many-body formalisms that already exist or are yet to be formulated. Program summary Program Title: ADG CPC Library link to program files: http://dx.doi.org/10.17632/6h4xrydwfb.2 Licensing provisions: GPLv3 Programming language: Python3 Journal reference of previous version: P. Arthuis, T. Duguet, A. Tichai, R.-D. Lasseri and J.-P. Ebran, ”ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory”, Computer Physics Communications 240 (2019), pp. 202-227. Does the new version supersede the previous version?: Yes. Reasons for the new version: Incorporation of a new formalism into the program. Summary of revisions: Addition of off-diagonal BMBPT to the formalisms for which diagrams can be generated, fix of a wrong symmetry factor, move of the codebase from Python2 to Python3 while maintaining support for Python2, various optimizations to reduce the time and memory necessary to the program. Nature of problem: As formal and numerical developments in many-body-perturbation-theory-based ab initio methods make higher orders reachable, manually producing and evaluating all the diagrams becomes rapidly untractable as both their number and complexity grow quickly, making it prone to mistakes and oversights. Solution method: Diagonal BMBPT diagrams are encoded as square matrices known as oriented adjacency matrices in graph theory, and then turned into graph objects using the NetworkX package. Off-diagonal BMBPT diagrams can then be generated from those graphs. Checks on the diagrams and evaluation of their time-integrated expression are eventually done on a purely diagrammatic basis. HF-MBPT diagrams are produced and evaluated as well using the same principle.

中文翻译：

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ADG：多体图的自动生成和评估 II。粒子数投影 Bogoliubov 多体摄动理论

摘要 我们描述了代码 ADG 的第二个版本 (v2.0.0)，它自动 (1) 生成所有有效的非对角 Bogoliubov 多体微扰理论图在粒子数投影 Bogoliubov 多体微扰理论 (PNP-BMBPT) 中起作用) 和 (2) 评估它们的代数表达式以用于数值应用。对于同时包含二体（四条腿）和三体（六条腿）相互作用（顶点）的哈密顿量，这是在任何微扰阶 p 下实现的。所有有效的 p 阶非对角 BMBPT 图都是从一组对角线，即未投影的 BMBPT 图系统地生成的。Arthuis 等人详细描述了后者的生产。(2019) 处理 ADG 的第一个版本。非对角 BMBPT 图的自动评估既依赖于代数费曼规则的应用，也依赖于提供剩余 p 元组时间积分结果的强大图解规则的识别。新的图解规则概括了 Arthuis 等人已经确定的规则。(2019) 独立于微扰顺序和拓扑评估对角线 BMBPT 图。代码 ADG 是用 Python3 编写的，并使用了图形操作包 NetworkX。该代码保持足够的灵活性，以便在这些年中进一步扩展，以解决已经存在或尚未制定的各种多体形式中的图表。程序摘要程序名称：ADG CPC 库程序文件链接：http://dx.doi.org/10.17632/6h4xrydwfb.2 许可条款：GPLv3 编程语言：以前版本的 Python3 期刊参考：P. Arthuis, T. Duguet, A. Tichai, R.-D. 拉塞里和 J.-P. Ebran，“ADG：多体图的自动生成和评估 I. Bogoliubov 多体微扰理论”，Computer Physics Communications 240 (2019)，第 202-227 页。新版本是否取代以前的版本？：是的。新版本的原因： 将新的形式主义纳入程序。修订摘要：将非对角线 BMBPT 添加到可以生成图表的形式中，修复错误的对称因子，将代码库从 Python2 移动到 Python3，同时保持对 Python2 的支持，各种优化以减少所需的时间和内存到程序。问题性质：随着基于多体微扰理论的 ab initio 方法的形式和数值发展使更高阶变得可达到，手动生成和评估所有图表变得很快变得难以处理，因为它们的数量和复杂性都在快速增长，使其容易出错和疏忽。解决方法：对角线BMBPT图被编码为图论中称为定向邻接矩阵的方阵，然后使用NetworkX包转化为图对象。然后可以从这些图生成非对角线 BMBPT 图。对图表的检查和对其时间积分表达式的评估最终是在纯粹的图表基础上完成的。HF-MBPT 图也使用相同的原理生成和评估。手动生成和评估所有图表变得很快变得难以处理，因为它们的数量和复杂性都在快速增长，容易出错和疏忽。解决方法：对角线BMBPT图被编码为图论中称为定向邻接矩阵的方阵，然后使用NetworkX包转化为图对象。然后可以从这些图生成非对角线 BMBPT 图。对图表的检查和对其时间积分表达式的评估最终是在纯粹的图表基础上完成的。HF-MBPT 图也使用相同的原理生成和评估。手动生成和评估所有图表变得很快变得难以处理，因为它们的数量和复杂性都在快速增长，容易出错和疏忽。解决方法：对角线BMBPT图被编码为图论中称为定向邻接矩阵的方阵，然后使用NetworkX包转化为图对象。然后可以从这些图生成非对角线 BMBPT 图。对图表的检查和对其时间积分表达式的评估最终是在纯粹的图表基础上完成的。HF-MBPT 图也使用相同的原理生成和评估。然后使用 NetworkX 包转换为图形对象。然后可以从这些图生成非对角线 BMBPT 图。对图表的检查和对其时间积分表达式的评估最终是在纯粹的图表基础上完成的。HF-MBPT 图也使用相同的原理生成和评估。然后使用 NetworkX 包转换为图形对象。然后可以从这些图生成非对角线 BMBPT 图。对图表的检查和对其时间积分表达式的评估最终是在纯粹的图表基础上完成的。HF-MBPT 图也使用相同的原理生成和评估。