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 ne
gative 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.
