  In this manuscript we investigate the one-dimensional anisotropic XY model
with ferromagnetic and antiferromagnetic interactions, which gives more
interesting phase diagrams and dynamic critical behaviors. By using quantum
renormalization-group method, we find that there are three phases in the
system: antiferromagnetic Ising phase ordered in "x direction", spin-fluid
phase and ferromagnetic Ising phase ordered in "y direction". In order to study
the dynamical critical behaviors of the system, two quantum quenching methods
are used. In both cases, the concurrence, a measure of entanglement, oscillates
periodically over time. We show that the periods are the same and can be used
as a new order parameter for quantum phase transitions. For further discussion,
we derive the scaling exponent, {\theta}, and correlation length exponent,
{\nu}, from the scaling behavior of the evolution period.
