  We investigate the relaxation dynamics of the fermion two-point correlation
function $C_{mn}(t)=\langle\psi(t)|c_{m}^{\dag}c_{n}|\psi(t)\rangle$ in the XY
chain with staggered nearest-neighbor hopping interaction after a quench. We
find that the deviation $\delta C_{mn}(t)=C_{mn}(t)-C_{mn}(\infty)$ decays with
time following the power law behavior $t^{-\mu}$, where the exponent $\mu$
depends on whether the quench is to the commensurate phase ($\mu=1$) and
incommensurate phase ($\mu=\frac{1}{2}$). This decay of $\delta C_{mn}(t)$
arises from the transient behavior of the double excited quasiparticle
occupations and the transitions between different excitation spectra.
Furthermore, we find that the steady value $C_{mn}(\infty)$, which is different
from the ground state expectation value, only involves the average fermion
occupation numbers (i.e. the average excited single particle). We also observe
nonanalytic singularities in the steady value $C_{mn}(\infty)$ for the quench
to the critical points of the quantum phase transitions (QPTs), suggesting its
potential use as a signature of QPTs.
