Interplay of spin-orbit and entropic effects in Cerium

We perform first-principle calculations of elemental cerium and compute its pressure-temperature phase diagram, finding good quantitative agreement with the experiments. Our calculations indicate that, while a signature of the volume-collapse transition appears in the free energy already at low temperatures, at larger temperatures this signature is enhanced because of the entropic effects, and originates an actual thermodynamical instability. Furthermore, we find that the catalyst determining this feature is --- in all temperature regimes --- a pressure-induced effective reduction of the $f$-level degeneracy due to the spin-orbit coupling. Our analysis suggests also that the lattice vibrations might be crucial in order to capture the behavior of the pressure-temperature transition line at large temperatures.