  We propose two complimentary numerical methods for rigorous computation of
dynamic structure factor at zero temperature. One solution is to solve
Schrodinger equation using time dependent variational principle (TDVP) with
matrix product states (MPSs) proposed by Haegeman el al. [Physical Review B 94,
165116], and Fourier transform correlation functions in time to frequency
domain. Another way is to directly compute the transition rate between the
ground state and several low lying momentum eigenstates that are accessed using
MPSs method amended with momentum filtering process. We benchmark both methods
on a spin-1/2 Antiferromagnetic (AF) Heisenberg chain with periodic boundary
condition. With finite size scaling analysis, the asymptotic line shape as a
function of {\omega} can be reproduced at various momentum k with both methods.
