  We consider the spin-1/2 anisotropic XY chain in a transverse (z) field with
the Dzyaloshinskii-Moriya interaction directed along z-axis in spin space to
examine the effect of the Dzyaloshinskii-Moriya interaction on the zz, xx and
yy dynamic structure factors. Using the Jordan-Wigner fermionization approach
we analytically calculate the dynamic transverse spin structure factor. It is
governed by a two-fermion excitation continuum. We analyze the effect of the
Dzyaloshinskii-Moriya interaction on the two-fermion excitation continuum.
Other dynamic structure factors which are governed by many-fermion excitations
are calculated numerically. We discuss how the Dzyaloshinskii-Moriya
interaction manifests itself in the dynamic properties of the quantum spin
chain at various fields and temperatures.
