ADG: Automated generation and evaluation of many-body diagrams II. Particle-number projected Bogoliubov many-body perturbation theory
ADG: Automated generation and evaluation of many-body diagrams II. Particle-number projected Bogoliubov many-body perturbation theory
复制标题
ADG：多体图的自动生成和评估 II。
DOI：
10.1016/j.cpc.2020.107677
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发表时间：
2021
影响因子：
6.3
通讯作者：
Arthuis P
中科院分区：
文献类型：
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作者：
Arthuis P
我们描述第二个版本（v2。0.0)ADG程序自动地（1）生成在粒子数投影Bogoliubov多体微扰理论（PNP-BMBPT）中起作用的所有有效的非对角Bogoliubov多体微扰理论图，（2）计算它们的代数表达式，以用于数值应用。这是实现在任何微扰阶p的哈密顿量包含两个身体（四腿）和三体（六腿）相互作用（顶点）。所有有效的非对角BMBPT图的顺序p系统地产生从一组对角，即，未投影，BMBPT图。后者的生产在Arthuis et al.（2019）处理ADG的第一个版本。非对角BMBPT图的自动化评价依赖于代数费曼规则的应用和提供剩余p-元组时间积分的结果的强大的图解规则的识别。新的图解规则推广了Arthuis等人已经确定的规则。（2019）独立于其微扰阶和拓扑来评估对角BMBPT图。代码ADG是用Python3编写的，并使用了图形操作包NetworkX。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主义中的数学问题。程序摘要程序标题：ADG CPC库程序文件链接：https：//doi。org/10.17632/6h4xrydwfb. 2许可条款：GPL v3编程语言：Python 3上一版本期刊参考：P. Arthuis，T. Duguet，A. Tichai河，D. Lasseri和J. - P. Ebran，”ADG：多体图的自动生成和评估I。Bogoliubov多体微扰理论”，计算机物理通信240（2019），pp。202-227.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：添加非对角BMBPT到可以生成图的形式主义中，修复错误的对称因子，将代码库从Python 2移动到Python 3，同时保持对Python 2的支持，各种优化以减少程序所需的时间和内存。问题性质：由于基于多体微扰理论的从头算方法的形式和数值发展使得更高的阶数可以达到，手动生成和评估所有图变得越来越难以驾驭，因为它们的数量和复杂性都在迅速增长，容易出现错误和疏忽。解决方法：对角BMBPT图被编码为在图论中称为定向邻接矩阵的方阵，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BMBPT图。检查的图表和评估其时间积分表达式最终完成一个纯粹的图表的基础上。HF-MBPT图的制作和评价，以及使用相同的原则。
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, ie, 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: https://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.