@antoine-levitt This is a two dimensional tight-binding Hamiltonian for a large-scale TMD structure. Unfortunately, I need roughly the 30000-30020th eigenvalues out of 117090 eigenvalues, so determining all occupied states is not really an option. As mentioned by @stevengj, the sparsity is quite low. A good impression of the matrices:
@lmiq Thanks for bringing the paper to my attention. Do I understand correctly your method does not actually solve the eigenvalue equation? I have already finished mean-field self-consistent calculation with a third-party software and is now trying to do some analysis, so I really need the eigenvalues and eigenvectors.
I already have a reasonably working solution. Good for me to have a rough idea how eigs works.