Singularities in large deviations of work in quantum quenches

We investigate large deviations of the work performed in a quantum quench across two different phases separated by a quantum critical point, using as an example the Dicke model quenched from its superradiant to its normal phase. We extract the distribution of the work from the Loschmidt amplitude and compute for both the corresponding large-deviation forms. Comparing these findings with the predictions of the classification scheme put forward in Gambassi and Silva [Phys. Rev. Lett. 109, 250602 (2012)], we are able to identify a regime which is in fact distinct to the ones identified so far: here the rate function exhibits a nonanalytical point which is a strong indication of the existence of an out-of-equilibrium phase transition in the rare fluctuations of the work.