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The neon isotopic chain displays a rich phenomenology, ranging fromclustering in the ground-state of the self-conjugate doubly open-shell stable$^{20}$Ne isotope to the physics of the island of inversion around theneutron-rich $^{30}$Ne isotope. This second (i.e. Paper II) of the presentseries proposes an extensive ab initio study of neon isotopes based on twocomplementary many-body methods, i.e. the quasi-exact in-medium no-core shellmodel (IM-NCSM) and the projected generator coordinate method (PGCM) that isideally suited to capturing strong static correlations associated with shapedeformation and fluctuations. Calculations employ a state-of-the-art generationof chiral effective field theory Hamiltonians and evaluate the associatedsystematic uncertainties. In spite of missing so-called dynamical correlations,which can be added via the multi-reference perturbation theory proposed in thefirst paper (i.e. Paper I) of the present series, the PGCM is shown to be asuitable method to tackle the low-lying spectroscopy of complex nuclei. Still,describing the physics of the island of inversion constitutes a challenge thatseems to require the inclusion of dynamical correlations. This is addressed inthe third paper (i.e. Paper III) of the present series.

Multi-reference many-body perturbation theory for nuclei II -- Ab initio study of neon isotopes via PGCM and IM-NCSM calculations