  We use the time dependent variational matrix product state (tVMPS) approach
to investigate the dynamical properties of the single impurity Anderson model
(SIAM). Under the Jordan-Wigner transformation, the SIAM is reformulated into
two spin-1/2 XY chains with local magnetic fields along the z-axis. The chains
are connected by the longitudinal Ising coupling at the end points. The ground
state of the model is searched variationally within the space spanned by the
matrix product state (MPS). The temporal Green's functions are calculated both
by the imaginary and real time evolutions, from which the spectral information
can be extracted. The possibility of using the tVMPS approach as an impurity
solver for the dynamical mean field theory is also addressed. Finite
temperature density operator is obtained by the ancilla approach. The results
are compared to those from the Lanczos and the Hirsch-Fye quantum Monte-Carlo
methods.
