Add sigma t-J model

[Yue-Zhengyuan]

This PR adds the so-called "sigma t-J model", which changes the hopping term of the t-J model to

$$ (-t) \sum_{\langle i j \rangle, \sigma} \sigma (c^\dagger_{i\sigma} c_{j\sigma} + h.c.) = (-t) \sum_{\langle i j \rangle} (c^\dagger_{i\uparrow} c_{j\uparrow} - c^\dagger_{i\downarrow} c_{j\downarrow} + h.c.) $$

[codecov]

Codecov Report

Attention: Patch coverage is 0% with 14 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/models/hamiltonians.jl	0.00%	14 Missing ⚠️

Files with missing lines	Coverage Δ
src/MPSKitModels.jl	100.00% <ø> (ø)
src/models/hamiltonians.jl	23.94% <0.00%> (-2.62%)	⬇️

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[lkdvos]

It might be more convenient to simply give this function a different name, instead of trying to pass everything through the same functions and having to control it with keyword arguments?

[Yue-Zhengyuan]

Personally I think the difference from the usual t-J model is quite minor (although the physics changes a lot), so I don't quite want to make a new function to construct the Hamiltonian...

[lkdvos]

Maybe, but if you take that argument further, more or less all models are the same, all spin models are very similar, all fermionic models are, all spinfull fermionic models are, ...
I'm exaggerating to make a point of course, but you probably see what I mean.
I don't think people that are interested in the tJmodel automatically want to read the additional information about this specific extension to it, and given that the name is tJmodel it just seems fair to keep this separate.
Maybe just tJsigma_model could work?

My main problem with it however is that e_plusmin is SU(2) symmetric, and I might be mistaken but this version is not? Having a keyword there that fundamentally changes the operator feels a bit off to me.

[Yue-Zhengyuan]

Oh I did overlook the different symmetry between the two models, since I hardly use the SU(2) symmetry. Now I agree that these two models should be separated. Thanks for pointing this out!

[lkdvos]

Apologies for the delay, this slipped my attention.

Looks good to go for me, is there any chance you have a benchmark result for this model? Perhaps a groundstate energy for some easy/somewhat trivial parameterset? It would be nice to be able to have a test for this

[Yue-Zhengyuan]

Honestly I don't have a benchmark result. The σ t-J model is a somewhat artificial construction. Now I think it's better to leave this un-standard model out of a public package until its physical significance is widely recognized and a good benchmark result is available.