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Bogoliubov many-body perturbation theory under constraint
Annals of Physics ( IF 3 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.aop.2020.168358
P. Demol , M. Frosini , A. Tichai , V. Somà , T. Duguet

In order to solve the A-body Schr\"odinger equation both accurately and efficiently for open-shell nuclei, a novel many-body method coined as Bogoliubov many-body perturbation theory (BMBPT) was recently formalized and applied at low orders. Based on the breaking of U(1) symmetry associated with particle-number conservation, this perturbation theory must operate under the constraint that the average number of particles is self-consistently adjusted at each perturbative order. The corresponding formalism is presently detailed with the goal to characterize the behavior of the associated Taylor series. BMBPT is, thus, investigated numerically up to high orders at the price of restricting oneself to a small, i.e. schematic, portion of Fock space. While low-order results only differ by 2 - 3 % from those obtained via a configuration interaction (CI) diagonalization, the series is shown to eventually diverge. The application of a novel resummation method coined as eigenvector continuation further increase the accuracy when built from low-order BMBPT corrections and quickly converges towards the CI result when applied at higher orders. Furthermore, the numerically-costly self-consistent particle number adjustment procedure is shown to be safely bypassed via the use of a computationally cheap a posteriori correction method. Eventually, the present work validates the fact that low order BMBPT calculations based on an a posteriori (average) particle number correction deliver controlled results and demonstrates that they can be optimally complemented by the eigenvector continuation method to provide results with sub-percent accuracy. This approach is, thus, planned to become a workhorse for realistic ab initio calculations of open-shell nuclei in the near future.

中文翻译:

约束条件下的 Bogoliubov 多体摄动理论

虽然低阶结果与通过配置交互 (CI) 对角化获得的结果仅相差 2-3%,但该系列最终会出现分歧。当从低阶 BMBPT 校正构建时,新的求和方法的应用进一步提高了准确度,并在以更高阶应用时快速收敛到 CI 结果。此外,通过使用计算成本低廉的后验校正方法,可以安全地绕过数值昂贵的自洽粒子数调整程序。最终,目前的工作验证了一个事实,即基于后验(平均)粒子数校正的低阶 BMBPT 计算提供了受控结果,并证明它们可以通过特征向量连续方法进行最佳补充,以提供具有亚百分比精度的结果。因此,这种方法计划在不久的将来成为开壳核的实际 ab initio 计算的主力。
更新日期:2021-01-01
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