Particle number density not enforced in `hubbard_model` Hamiltonian

[leburgel]

The docstring and signature of the hubbard_model Hamiltonian indicate that an integer particle number density can be imposed through the n keyword argument. However, this is not actually used in the implementation, so we always return a Hamiltonian with zero filling contrary to what the docstring says.

We should implement the proper uniform filling, which boils down to translating the integer n to the appropriate sector for the chosen symmetry shifting the Hamiltonian using MPSKit.add_physical_charge.

[lkdvos]

I just remembered why this is the case:

I think I looked at this and got stuck on the proper way to do it, because MPSKit had/has no public implementation of this. What bothered me the most though is that if we silently start shifting charges, we also have to tell users that any other operator, correlator, ... has to now have operators with shifted charges as well, and again, we are not providing the functionality to do so. (This is not a good reason to not do it, it's just slightly more involved than I initially expected I think).
After this I was considering if it might be worth it to actually insert a site in the unit cell to carry these charges, instead of merging it into the physical space. This avoids the redefined physical spaces, but now we have to offset site indices, so again that kind of sucks.
Afterwards, I thought maybe we could have a dedicated charged state type, where we pick a convention and work through everything, which might be the best way to do it, but also involves a lot of work, and since I didn't need this myself, I think I prioritized other things.

All this to say: we should definitely try and solve this, and I think it is both useful to have and important for the library(ies), but it is slightly more subtle than it looks from the surface.
Probably though most of this can be massively improved with a section in the docs and then we don't necessarily have to fully deal with all of this at the library level

[leburgel]

Having a dedicated charged state type is definitely the best option, but I don't think it's necessary to wait for this. I think not having the option of setting a particle density is technically still a bit worse than being able to set a particle number density and then not really knowing how to deal with this. So I would go with implementing it in the simplest way, which would be silently shifting the charges, after which we can worry about a good explanation of what this means so that it's actually usable.

[Yue-Zhengyuan]

I'd also like to implement the density shift in t-J model. I can follow up after the Hubbard model is updated.