Dear Negin,
One can turn off all the symmetries in the ED solver or solve for all the symmetry sectors separately. It is definitely better to utilize the symmetries (at least momentum and/or local symmetries) if they are conserved. Therefore, while it depends on the kind of problem you are interested in, I suggest to do ED in each sector and then collect the eigenvectors if needed.
As a side note:
I do suggest that you implement a simple ED code with your programming language of choice. Doing so might be a bit slow but does give you a lot of intuition into how these computations work, teaches you more about the physics, and also simplifies your way to make use of better written, more reviewed, and faster code (such as the ones implemented in ALPS) much more efficiently.
Honestly, starting from scratch, with no prior experience it should not take you more than a few days. Happy coding :)
On Wed, Apr 8, 2020, 12:40 PM Matthias Troyer troyer@phys.ethz.ch wrote:
If you need all eigenvectors in the full basis then turn all conserved quantum numbers and all symmetries (e.g. translation symmetry ) off
Matthias
On Apr 8, 2020, at 1:18 AM, Negin Mohseni monfarednegin@gmail.com
wrote:
Dear All,
Firstly I thank Rongyang for his fruitful explanation and suggestions.
He assured me that I had thought correctly. In fact, in our work I must have all eigenvectors of a system. For this reason, I read tutorials related to exact diagonalization (ED) from sparse diagonalization to full diagonalization. Unfortunately, none of them fulfills my need.
In most of tutorials the energy eigenvalues are sorted in several
subspaces and momentums categories. But, I just wish to have a data set containing eigenvectors ignoring the dependence of momentum or subspaces. For example, for Ising chain in a transverse field ("h"), I wish to have the system's eigenvectors (as a list) and corresponded eigenvalues for each "h".
How can we able to have a system's eigenvectors and corresponded
eigenvalues?
All the best
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