Dynamics following a linear ramps in the $O(N)$ model: dynamical transition and statistics of excitations

Abstract: Non-thermal dynamical critical behavior can arise in isolated quantum systems brought out of equilibirum by a change in time of their parameters. While this phenomenon has been studied in a variety of systems in the case of a sudden quench, here we consider its sensitivity to a change of protocol by considering the experimentally relevant case of a linear ramp in time. Focusing on the $O(N)$ model in the large $N$ limit, we show that a dynamical phase transition is always present for all ramp durations and discuss the resulting crossover between the sudden quench transition and one dominated by the equilibrium quantum critical point. We show that the critical behavior of the statistics of the excitations, signaling the non-thermal nature of the transition are robust against changing protocol. An intriguing crossover in the equal time correlation function, related to an anomalous coarsening is also discussed.