  We present the first application of the newly developed EKK theory of the
effective nucleon-nucleon interaction to shell-model studies of exotic nuclei,
including those where conventional approaches with fitted interactions
encounter difficulties. This EKK theory enables us to derive the interaction
suitable for several major shells ($sd$+$pf$ in this work). By using such an
effective interaction obtained from the Entem-Machleidt QCD-based
$\chi\mathrm{N}^3\mathrm{LO}$ interaction and the Fujita-Miyazawa three-body
force, the energies, E2 properties and spectroscopic factors of low-lying
states of neutron-rich Ne, Mg and Si isotopes are nicely described, as the
first shell-model description of the "island of inversion" without fit of the
interaction. The long-standing question as to how particle-hole excitations
occur across the $sd$-$pf$ magic gap is clarified with distinct differences
from the conventional approaches. The shell evolution is shown to appear
similarly to earlier studies.
