  Photoexcited GeTe undergoes a non-thermal phase transition from a
rhombohedral to a rocksalt crystalline phase. The microscopic mechanism and the
nature of the transition are unclear. By using constrained density functional
perturbation theory and by accounting for quantum anharmonicity within the
stochastic self-consistent harmonic approximation, we show that the non-thermal
phase transition is strongly first order and does not involve phonon softening,
at odd with the thermal one. The transition is driven by the closure of the
single particle gap in the photoexcited rhombohedral phase. Finally, we show
that ultrafast X-ray diffraction data are consistent with a coexistence of the
two phases, as expected in a first order transition. Our results are relevant
for the understanding of phase transitions and bonding in phase change
materials.
