Hi,

I am trying to study some dynamics using ITensor and I was wondering what is the most stable combination of functions.

To fix the ideas, I am considering the open Ising spin 1/2 chain in the gapped phase (h transverse field > 1) with N=100 sites. The groundstate is found very efficiently with the dmrg function of ITensor with a small number of sweeps; for the case I am considering (h = 1.5), I obtain high accuracy with a bond dimension of 5 at most.

Now, I am trying to perform some dynamics on this state. In order to do so, I am using the bult-in function fitapplyMPO with imaginary time. What I noticed is that even though I evolve with the same MPO Hamiltonian I used to find the groundstate, the bond dimension starts to grow. In principle, the state should not evolve at all as it is the groundstate of the Hamiltonian.

This effect is suppressed if I take a very small timestep (t=0.001) for the time-evolution.

I was wondering: is this the expected behaviour, which is essentially unavoidable, or it is a bad idea to combine the dmrg function and then the fitapplyMPO?

I was thinking that using imaginary time evolution e^{- tau H} to find the groundstate still with fitapplyMPO could avoid this issue, even though it would provide a worse description of the groundstate.

What do you think?