@b3m2a1 This is a purely mathematical problem, not taken from physics. I carefully looked through the algorithm, trying to find some clues, and also looked for them in alternative algorithms - this problem is not solved, but intuition tells the area in which to look for the answer.
I have a matrix $M$ in Bloch basis (momentum space). Then I have to take Fourier transform of $M$ to go to real space. The size of this lattice in real space can be fixed to some value $N_{unit}$.
Furthermore, I have to determine the eigenvectors of this real space matrix and study dynamics so it...