  We investigate the possibility and impacts of a first-order phase transition
from hadronic matter to quark matter in neutron stars (NSs) using two specific
models: the parity doublet model (PDM) for the hadronic phase and the
Nambu-Jona-Lasinio (NJL) type model for the quark phase. By combining these
models, we construct hybrid equations of state (EOSs) that capture the
transition between the two phases. We explore the parameter space of both
models to identify the conditions under which a first-order phase transition
can occur and study its effects on NS properties. We identify the suitable
parameter space and constrain the onset density of the first-order phase
transition. For $m_0$ = 500 MeV -- the chiral invariant mass in PDM, the phase
transition occurs between 1.9$n_0$ and 2.95$n_0$ and ends between 2.1$n_0$ and
3.6$n_0$. Increasing $m_0$ to 600 MeV shifts the phase transition to higher
densities, occurring between 2.9$n_0$ and 4.1$n_0$ and ending between 3.4$n_0$
and 4.6$n_0$.
