I am trying to calculate the optical conductivity in the 1D Hubbard model (1 px, 2 py, 2 pz, and 1 d orbital), which involves time-evolving the system, calculating the current-current correlator of time-step t with step 0.
My friend is doing Exact Diagonalization and we have reached agreement in our results on all non-time evolved ground state quantities: energy, expectation values of all creation-annihilation operator combinations, and even the current-current correlator. However, our time evolutions are giving drastically different results, and there is strong reason to believe his are correct and mine are incorrect.
I am just trying to time-evolve with the ground state Hamiltonian, and whether I use fitApplyMPO, exactApplyMPO, MPS or IQMPS, and normalize at each step or don't, my results are still quite bad. The time evolution is very evidently not smooth, even using time steps of 0.02, and supplying a cutoff of 1e-13, and allowing for max bond dimension of 100,000... First off, I get completely different results when I keep everything as IQMPS and time evolve with an IQMPO than when I convert to MPS/MPO and time evolve. These differences appear even after the first time step. Second, they occur whether I use open or periodic boundary conditions, and regardless of the quantum number sector I am in.
In all cases, my t=0 results align precisely with ED results, and my t>0 results fail to resemble anything reasonable.
Furthermore, when I evolve more than a few time steps, I start to get diagHermitian errors from my time-evolution.
Anybody have any insight into what is going on?