Ab initio nuclear shape coexistence and emergence of island of inversion around $N=20$

We extend a nuclear ab initio framework based on chiral two- and three-nucleon interactions to investigate shape coexistence and the degradation of the $N=20$ magic number in both even-even and odd-even magnesium isotopes. The quantum-number projected generator coordinate method, combined with the in-medium similarity renormalization group (IMSRG), is employed to compute their low-lying states. This approach reasonably reproduces the coexistence of weakly and strongly deformed states at comparable energies, and allows us to track the emergence of the $N=20$ island of inversion through the continuous IMSRG evolution of the chiral Hamiltonian. Our results indicate that the ground state of $^{33}$Mg with spin-parity $3/2^-$ is predominantly a strongly deformed configuration with $K^\pi = 3/2^-$, while the lowest $7/2^-$ state is predicted to be a shape isomer, consisting of a mixture of weakly deformed configurations with different $K$ values. The results highlight the essential roles of both dynamical and static collective correlations in reproducing the ordering of nuclear states with distinct shapes.