Asking in google "quantum break" arxiv gives a number of physics preprints,
This seems relevant to gravity:
Quantum break in high intensity gravitational wave interactions
The lowest order amplitudes for [graviton+graviton→photon+photon] lead to cross-sections of order G2, where G is the gravitational constant. These are too small to be of any interest. However in dense clouds of pure gravitons there are collective effects utilizing these same amplitudes that under the right circumstances can lead to copious production of photons.
In the pdf it states:
The comparative suddenness of the transition earns it the designation of "quantum break"
So it is a collective phenomenon which under the right circumstances leads to a sudden copious production of photons., as far as I can see. Quantum because it needs quantum mechanics to get the effect.
In an axion paper:
Once we include self-interaction of the axion, the quantum state evolves so that the expectation value over it starts to deviate from the classical solution. The time-scale of this process defines the quantum break-time.
So it seems to be used to define when quantum effects take over.