\textit{Ab initio} study in the island of inversion within the two-major-shell valence space

Abstract: We present an \textit{ab initio} study of nuclear structure in the island of inversion around neutron number $N=20$, using multishell effective Hamiltonians derived from valence-space in-medium similarity renormalization group approach combined with the quantum-number projected generator coordinate method. By progressively expanding the valence space from the \textit{sd} shell to the intermediate $sdf_{7/2}p_{3/2}$ space and, for the first time, to the full \textit{sdfp} shell, we investigate low-lying spectra, $E2$ transition strengths, deformation properties, and neutron occupancies in even-even Ne, Mg, and Si isotopes around $N=20$. Our results show that enlarging the valence space significantly improves the description of quadrupole collectivity, yielding better agreement with experimental data for key observables such as the lowered $2^+$ energies and the enhanced $B(E2;0^+_1\rightarrow2_1^+)$ values. The analysis reveals the critical role of cross-shell multi-particle multi-hole excitations in breaking the $N=20$ shell closure and establishing intruder-dominated ground states. It also demonstrates the ability of the VS-IMSRG+PGCM framework to capture both dynamical (short range) and static (long range) correlations across multiple major-oscillator shells.