Dynamical relaxation behaviors of a critical quench

We study the universal dynamical relaxation behaviors of a quantum XY chain following a quench, paying special attention to the case that the prequenched Hamiltonian, or the postquenched Hamiltonian, or both of them are at critical points of equilibrium quantum phase transitions. In such ``critical quench", we find very interesting real-time dynamical scaling behaviors and the crossover phenomena between them. For a quench from a noncritical point to a critical point, we find that, compared to the noncritical quench, the universal power-law scaling behavior does not change; however, there may be a crossover between the exponential decaying behavior and the power-law scaling. For a quench from a critical point to a noncritical point, the power-law scaling behaviors $t^{-3/2}$ and $t^{-3/4}$ in the noncritical quenches may be changed to $t^{-1}$ and $t^{-1/2}$, respectively. If the prequenched Hamiltonian is set to be a point that is close to but not exactly at a critical point, we find interesting crossover phenomena between different power-law scaling behaviors. We also study the quench from the vicinity of a multicritical point, we find crossover behaviors that are induced by a different mechanism, and new crossover exponent is found. All the results are related to the gap-closing properties of the energy spectrum of the critical points.