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We construct a model to describe dense hadronic matter at zero and finite temperature, based on the parity doublet model of DeTar and Kunihiro, with including the iso-singlet scalar meson σ as well as ρ and ω mesons. We show that, by including a six-point interaction of σ meson, the model reasonably reproduces the properties of the normal nuclear matter with the chiral invariant nucleon mass m0 in the range from 500 MeV to 900 MeV. Furthermore, we study the phase diagram based on the model, which shows that the value of the chiral condensate drops at the liquid-gas phase transition point and at the chiral phase transition point. We also study asymmetric nuclear matter and find that the first order phase transition for the liquid-gas phase transition disappears in asymmetric matter and that the critical density for the chiral phase transition at non-zero density becomes smaller for larger asymmetry.

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