Example Request: Generation of symmetry TOML files

[andrewkhardy]

Thank you so much for making XDiag public and congratulations on the arXiv posting. As I'm learning by going through the examples, I'm wondering if one could add an example about how to generate the symmetry TOML files such as this one for the triangular Heisenberg lattice. Some of this is in the documentation here, but there's clearly a script that was used to create such a file and if you would like to do things like change the number of sites, you would need to recreate such a file. Could you add an example of how to generate a file of characters / irreps and so on?

[awietek]

Dear Andrew,

thank you for your interest in XDiag and your suggestion. Indeed, it would be useful to have an example how to create the representations and symmetry permutations and we will put in on our TODO list. The permutation group and representations need not necessarily be read from a TOML file and can also be constructed within the code. Here, we do feature a couple of examples how to create them, see e.g. here https://awietek.github.io/xdiag/examples/spinhalf_chain_gs_corr_symmetries/

So one could translate this example into a small script that creates a TOML file instead and reads it in. If you could help us with this, we would be very happy :)

The triangular lattice case is a bit more involved, as here we are also using point group and translation symmetries. To get a complete set of representations, one must consider concepts like Little groups and work out the representation theory for the specific group. Currently, the user has to input this by hand. It's not that difficult, but one needs to have a grasp on group representation theory, which is anyway recommended when using symmetries.

Best,

Alex

[andrewkhardy]

Dear Alex,

I'll take a look and see about an example PR if I have something nice, thank you for your quick response.

Andrew