  The $\alpha$-$\gamma$ transition in cerium has been studied in both zero and
finite temperature by Gutzwiller density functional theory. We find that the
first order transition between $\alpha$ and $\gamma$ phases persists to the
zero temperature with negative pressure. By further including the entropy
contributed by both electronic quasi-particles and lattice vibration, we obtain
the total free energy at given volume and temperature, from which we obtain the
$\alpha$-$\gamma$ transition from the first principle calculation. We also
computed the phase diagram and pressure versus volume isotherms of cerium at
finite temperature and pressure, finding excellent agreement with the
experiments. Our calculation indicate that both the electronic entropy and
lattice vibration entropy plays important role in the $\alpha$-$\gamma$
transition.
