  In spite of missing dynamical correlations, the projected generator
coordinate method (PGCM) was recently shown to be a suitable method to tackle
the low-lying spectroscopy of complex nuclei. Still, describing absolute
binding energies and reaching high accuracy eventually requires the inclusion
of dynamical correlations on top of the PGCM. In this context, the present work
discusses the first realistic results of a novel multi-reference perturbation
theory (PGCM-PT) that can do so within a symmetry-conserving scheme for both
ground and low-lying excited states. First, proof-of-principle calculations in
a small ($e_{\mathrm{max}}=4$) model space demonstrate that exact binding
energies of closed- (\nucl{O}{16}) and open-shell (\nucl{O}{18}, \nucl{Ne}{20})
nuclei are reproduced within $0.5-1.5\%$ at second order, i.e. through
PGCM-PT(2). Moreover, profiting from the pre-processing of the Hamiltonian via
multi-reference in-medium similarity renormalization group transformations,
PGCM-PT(2) can reach converged values within smaller model spaces than with an
unevolved Hamiltonian. Doing so, dynamical correlations captured by PGCM-PT(2)
are shown to bring essential corrections to low-lying excitation energies that
become too dilated at leading order, i.e., at the strict PGCM level. The
present work is laying the foundations for a better understanding of the
optimal way to grasp static and dynamical correlations in a consistent fashion,
with the aim of accurately describing ground and excited states of complex
nuclei via ab initio many-body methods.
