\begin{document}$ N=28 $\end{document}, have attracted extensive experimental and theoretical interest. We utilize the ab initio valence-space in-medium similarity renormalization group approach, based on chiral nucleon-nucleon and three-nucleon forces, to investigate the exotic properties of these isotopes. Systematic calculations of the low-lying spectra are performed. A key finding is the level inversion between \begin{document}$ 3/2_1^+ $\end{document} and \begin{document}$ 1/2_1^+ $\end{document} states in odd-A isotopes, attributed to the inversion of \begin{document}$ \pi 0d_{3/2} $\end{document} and \begin{document}$ \pi 1s_{1/2} $\end{document} single-particle states. The ab initio calculations, which incorporate the three-nucleon forces, correlate closely with existing experimental data. Further calculations of effective proton single-particle energies provide deeper insights into the shell evolution for \begin{document}$ Z=14 $\end{document} and \begin{document}$ 16 $\end{document} sub-shells. Our results indicate that the three-body force plays important roles in the shell evolution for \begin{document}$ Z=14 $\end{document} and \begin{document}$ 16 $\end{document} sub-shells with neutron numbers ranging from 20 to 28. Additionally, systematic ab initio calculations are conducted for the low-lying spectra of odd-odd nuclei. The results correspond with experimental data and provide new insights for future research into these isotopes up to and beyond the drip line."> <i>Ab initio</i> valence-space in-medium similarity renormalization group calculations for neutron-rich P, Cl, and K isotopes -
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