Dynamical quantum phase transitions in the random field Ising model

Over the last few years it was pointed out that certain observables of time-evolving quantum systems may have singularities at certain moments in time, mimicking the singularities physical systems have when undergoing phase transitions. These were given the name of dynamical phase transitions. They were shown to exist in certain integrable (exactly solvable) quantum systems, and were seen numerically and experimentally in some models which were not integrable. The universality classes of such singularities were not yet convincingly established, however. We argue that random field Ising models feature singularities in time which may potentially be present in a wider variety of quantum systems, in particular in those which are many-body localized, and describe these singularities in detail analytically.