  We investigate the emergence of universal dynamical scaling in quantum
critical spin systems adiabatically driven out of equilibrium, with emphasis on
quench dynamics which involves non-isolated critical points (i.e., critical
regions) and cannot be a priori described through standard scaling arguments
nor time-dependent perturbative approaches. Comparing to the case of an
isolated quantum critical point, we find that non-equilibrium scaling behavior
of a large class of physical observables may still be explained in terms of
equilibrium critical exponents. However, the latter are in general
non-trivially path-dependent, and detailed knowledge about the time-dependent
excitation process becomes essential. In particular, we show how multiple level
crossings within a gapless phase may completely suppress excitation depending
on the control path. Our results typify non-ergodic scaling in continuous
finite-order quantum phase transitions.
