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We investigate the emergence of universal dynamical scaling in quantumcritical spin systems adiabatically driven out of equilibrium, with emphasis onquench dynamics which involves non-isolated critical points (i.e., criticalregions) and cannot be a priori described through standard scaling argumentsnor time-dependent perturbative approaches. Comparing to the case of anisolated quantum critical point, we find that non-equilibrium scaling behaviorof a large class of physical observables may still be explained in terms ofequilibrium critical exponents. However, the latter are in generalnon-trivially path-dependent, and detailed knowledge about the time-dependentexcitation process becomes essential. In particular, we show how multiple levelcrossings within a gapless phase may completely suppress excitation dependingon the control path. Our results typify non-ergodic scaling in continuousfinite-order quantum phase transitions.

Dynamical non-ergodic scaling in continuous finite-order quantum phase transitions