Bogoliubov many-body perturbation theory under constraint
| Autor: | Pepijn Demol, Mikael Frosini, Thomas Duguet, Vittorio Somà, Alexander Tichai |
|---|---|
| Přispěvatelé: | Institut de Recherches sur les lois Fondamentales de l'Univers (IRFU), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Nuclear Theory
[PHYS.NUCL]Physics [physics]/Nuclear Theory [nucl-th] higher-order Many-body theory General Physics and Astronomy 01 natural sciences Schrödinger equation Fock space symbols.namesake 0103 physical sciences Taylor series Applied mathematics Resummation 010306 general physics Eigenvalues and eigenvectors perturbation theory Physics ab initio Open-shell nuclei 010308 nuclear & particles physics Taylor expansion symmetry breaking: U(1) nucleus shell model particle number: conservation law resummation symbols many-body problem A priori and a posteriori Schroedinger equation Perturbation theory (quantum mechanics) |
| Zdroj: | Annals Phys. Annals Phys., 2021, 424, pp.168358. ⟨10.1016/j.aop.2020.168358⟩ |
| Popis: | 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. Comment: 45 pages, 10 figures; accepted version |
| Databáze: | OpenAIRE |
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