I have read this tutorial about MPS time evolution.
However, my chain Hamiltonian is time-dependent, for exmaple H(t)=\sum_j \cos (\omega t)h_{j,j+1}.
Because the Hamiltonians at different times do not commute, we can not make this decompose e^{-iH100\tau}|\psi_0\rangle=e^{-iH(100\tau)\tau}\cdots e^{-iH(\tau)\tau}|\psi_0\rangle.
How should we solve this problem? Is there any code that can be referenced?
Thank you very much for your attention
Look forward to your reply.
Regards.
YD Shen.
Note that even though the Hamiltonian might not commute with itself at different times, still the Trotter decomposition that you suggested above would be, to first order in \tau, correct.
That is because the first commutator (which is the leading order correction) appears with a prefactor of \tau^2. With that being said, you have to be aware of the typical time scale of the Hamiltonian and choose the time step by, roughly, the relation: