Starting from a chiral two- plus three-nucleon interaction, we perform a systematic study of the low-lying states of neutron-rich nuclei around $N=20$ using the in-medium generator coordinate method, which combines the multireference in-medium similarity renormalization group with the quantum-number projected generator coordinate method defined in a full single-particle space. The main features of the energy spectra and electromagnetic properties of low-lying states in both even-even and odd-mass nuclei of this mass region are reasonably reproduced. The boundary of the $N=20$ island of inversion (IOI) is investigated, and the results indicate that ${}^{30}\mathrm{Ne}, {}^{29,31,33}\mathrm{Na}, {}^{31,32,33,34}\mathrm{Mg}$, and ${}^{35}\mathrm{Al}$ lie within the IOI, whereas ${}^{29}\mathrm{F}, {}^{29}\mathrm{Ne}, {}^{30}\mathrm{Mg}, {}^{31,33}\mathrm{Al}, {}^{34,35}\mathrm{Si}$, and ${}^{35}\mathrm{P}$ fall outside it.

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• Nuclear structure & decays
• Ab initio calculations
• Many-body techniques