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.
Probability distribution of observables from a Bogoliubov vacuum projected onto good particle number: application to scission configurations of an actinide
Variational theory combining number-projected BCS and coupled-cluster doubles
基于耦合团簇和粒子数投影BCS模型，用变分方法高精度地描述了有限费米子系统中的基态配对关联。这种保持弹性的波函数的灵活性，使一个统一的图片有效的从弱到强耦合，无论是在小型和大型系统。本变分方法始终产生能量上限，同时以与非变分粒子数投影Bogoliubov耦合簇理论相同的精度水平操作[Phys. Rev. C 99，044301（2019）]。
Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation
有限温度的Hartree-Fock-Bogoliubov（HFB）近似经常破坏基础多体哈密顿量的对称性。通过变后投影将HFB配分函数的计算限制在具有良好量子数的子空间，恢复了在破坏这些对称性时丢失的一些相关性，尽管破坏对称性的影响（例如相变处的尖锐扭结）仍然存在。然而，在有限温度HFB近似中，最一般的投影后变分公式受到符号模糊性的限制。本文推广了L. M. Robledo在参考文献[1]中的方法来消除这种符号模糊性，并评估在最一般的HFB情况下变化后投影所需的更复杂的多体迹线。我们验证我们的方法，通过一个简单的模型中的粒子数投影HFB热能的原理证明计算。
