  Quasi-static transformations, or slow quenches, of many-body quantum systems
across quantum critical points create topological defects. The Kibble-Zurek
mechanism regulates the appearance of defects in a local quantum system through
a classical combinatorial process. However, long-range interactions disrupt the
conventional Kibble-Zurek scaling and lead to a density of defects that is
independent of the rate of the transformation. In this study, we analytically
determine the complete full counting statistics of defects generated by slow
annealing a strong long-range system across its quantum critical point. We
demonstrate that the mechanism of defect generation in long-range systems is a
purely quantum process with no classical equivalent. Furthermore, universality
is not only observed in the defect density but also in all the moments of the
distribution. Our findings can be tested on various experimental platforms,
including Rydberg gases and trapped ions.
