Dynamical relaxation of a long-range Kitaev chain

We study the universal real-time relaxation behaviors of a long-range Kitaev chain following a quench, and the results are compared to a short-range quantum XY chain. Our research includes both noncritical and critical quenches. In the case of noncritical quench, i.e., neither the initial state nor the postquench Hamiltonian is at a critical point of the 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 quantum 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 quantum XY 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.