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Abstract

In order to solve the A-body Schrodinger 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 behaviour 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 increases 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. (C) 2020 Elsevier
Inc. All rights reserved.