Dynamic structure factor from real time evolution and exact correction vectors with matrix product states

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.