On the accuracy of the adiabatic-impulse approximation

We study the adiabatic-impulse approximation as a tool to approximate the time evolution of quantum states when driven through a quantum critical point. The adiabatic-impulse approximation originates from the Kibble-Zurek (KZ) theory of non-equilibrium classical phase transitions,
more precisely from the KZ theory when applied to a continuous quantum phase transition. In this case, the KZ mechanism predicts the power-law scaling of the defect density as a function of the driving rate by which the system is driven across a continuous quantum phase transition. However, in this work, we quantify the accuracy of the adiabatic-impulse approximation for the time evolution of quantum systems and determine the conditions when this approximation performs better than the simple adiabatic approximation. Our findings are illustrated in driven closed and open quantum systems.