Dynamical critical scaling and effective thermalization in quantum quenches: Role of the initial state

We explore the robustness of universal dynamical scaling behavior in a quantum system near criticality with respect to initialization in a large class of states with finite energy. By focusing on a homogeneous XY quantum spin chain in a transverse field, we characterize the nonequilibrium response under adiabatic and sudden quench processes originating from a pure as well as a mixed excited initial state, and involving either a regular quantum critical or a multicritical point. We find that the critical exponents of the ground-state quantum phase transition can be encoded in the dynamical scaling exponents despite the finite energy of the initial state. In particular, we identify conditions on the initial distribution of quasiparticle excitation that ensure that Kibble-Zurek scaling persists. The emergence of effective thermal equilibrium behavior following a sudden quench toward criticality is also investigated, with focus on the long-time expectation value of the quasiparticle number operator. Despite the integrability of the XY model, this observable is found to behave thermally in quenches to a regular quantum critical point, provided that the system is initially prepared at sufficiently high temperature. However, a similar thermalization behavior fails to occur in quenches toward a multicritical point. We argue that the observed lack of thermalization originates in this case in the asymmetry of the impulse region that is also responsible for anomalous multicritical dynamical scaling.