  We study the universal real-time relaxation behaviors of a long-range quantum
XY chain following a quench. Our research includes both the noncritical and
critical quench. In the case of noncritical quench, i.e., neither the initial
state nor the postquench Hamiltonian is at a critical point of equilibrium
phase transition, a quench to the commensurate phase or incommensurate phase
gives a scaling of $t^{-3/2}$ or $t^{-1/2}$, respectively, which is the same as
the counterpart of the short-range XY model. However, for a quench to the
boundary line between the commensurate and incommensurate phases, the scaling
law $t^{-\mu}$ may be different from the $t^{-3/4}$ law of the counterpart of
the short-range model. More interestingly, the decaying exponent $\mu$ may
depend on the choice of the parameters of the postquench Hamiltonian because of
the different asymptotic behaviors of the energy spectrum. Furthermore, in
certain cases, the scaling behavior may be outside the range of predictions
made by the stationary phase approximation, because an inflection point emerges
in the energy spectrum. For the critical quench, i.e., the initial state or the
postquench Hamiltonian is at a critical point of equilibrium phase transition,
the aforementioned scaling law $t^{-\mu}$ may be changed because of the
gap-closing property of the energy spectrum of the critical point.
