论文标题
ADG：多体图的自动生成和评估II。粒子数投影Bogoliubov多体扰动理论
ADG: Automated generation and evaluation of many-body diagrams II. Particle-number projected Bogoliubov many-body perturbation theory
论文作者
论文摘要
我们描述了自动（1）自动生成所有有效的非对抗Bogoliubov的第二版（v2.0.0）。在粒子界投影的Bogoliubov多体扰动理论（PNP-BMBPT）（PNP-BMBPT）和（2）评估其eNGEBRAICERPERTINATION nUMEREDERPERIDERAIDS表达时，在粒子单上投影了多体扰动理论多体扰动理论图。这是在任何扰动订单$ p $中都可以实现的，其中包含两体（四腿）和三体（六腿）相互作用（顶点）。所有有效的OFFIAGONAL BMBPT订单$ P $的bmbpt图都是从对角线的集合中系统生成的，即未投影，BMBPT图。后者的生产在https://doi.org/10.1016/j.cpc.2018.11.023中详细描述。对基因BMBPT图的自动评估均取决于代数Feynman规则的应用，也依赖于确定强大的图形规则的识别，提供了其余$ p $ - 负时时间积分的结果。新的图形规则概括了在https://doi.org/10.1016/j.cpc.2018.11.023中已经确定的一条规则，以评估对角线BMBPT图独立于其扰动顺序和拓扑。代码ADG写在python3中，并使用图形操作软件包网络。多年来，该代码的灵活性足够灵活，可以进一步扩展，以解决已经存在或尚未制定的各种多体形式主义中的示意图。
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 https://doi.org/10.1016/j.cpc.2018.11.023 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 https://doi.org/10.1016/j.cpc.2018.11.023 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.
