Artifacts in Dynamical structure factor plots

ITensor Julia Questions
1

Hi Everyone,

I have an issue with the plotting the Dynamical Structure Factor (DSF). I have performed the calculations by the steps below:

  1. Compute the ground state with DMRG
  2. excite the ground state psi into |phi> = Sz | psi >
  3. Time evolve the original unexcited ground state and the excite state , so I have |psi(t)> and |phi(t)>
  4. Then, after each time evolutions step using TEBD, I would compute the correlations by putting an Sz at a specific site, lets say j, and contract all the indices; getting <psi(t)| Sz_j |phi(t)>
  5. I would then Fourier transform the plot in space
  6. Then , I would perform Linear prediction, similar to Barthel, Schollwock and White ([0901.2342] Spectral functions in one-dimensional quantum systems at T>0) before FT in time, to increase the resolution

However, I am finding that I have some artifacts in the plot, particularly at the lower frequencies. I have attached below the images if I perform linear prediction and if I do not, for the ferromagnetic Heisenberg model.

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The momentum range would be from [0,2pi] above.

Is it appropriate for me to subtract the mean of the signal for each column (each point in space), to reduce the large zero temporal frequency contribution in these plots?

2

One thing I noticed about your process for computing the Fourier transform is, did you also include any “broadening”? The most common type of broadening is to multiply your time-dependent correlation function by e^{-\alpha |t|} for some value of \alpha which will have the effect of replacing any singularities in your spectral function by Lorentizians of width \alpha. It can specifically help with issues related to long time behaviors of correlation functions.