Correlation properties of anisotropic XY model with a sudden quench

Starting from a general Hamiltonian which may undergo a quantum phase transition (QPT) with the change of a controllable parameter, we obtain a general conclusion that in a sudden quench system, when the final Hamiltonian is fixed, the behavior of the time-averaged expectation of any observable has close relationship with the gapless excitation of the initial Hamiltonian. To clarify our conclusion, we investigate the two-spin correlation of a XY chain in a transverse field under a sudden quench at zero temperature. The critical property of the derivative of quench two-spin correlation and the long-range correlation of the quench system are analyzed.