Change f_min_f_min convention

[Yue-Zhengyuan]

Previously, f_min_f_min was defined to be the same as adjoint(f_plus_f_plus), i.e. it is $(f^\dagger_1 f^\dagger_2)^\dagger = f_2 f_1$. Now I change it to $f_1 f_2$ (the negative of the original), which is the convention we use for other 2-body operators.

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[sanderdemeyer]

Good catch! The only small question I have is what the reason is for changing the sign of f_min_f_min and not of f_plus_f_plus?

[Yue-Zhengyuan]

Well, because f_plus_f_plus is already $f^\dagger_1 f^\dagger_2$ instead of $f^\dagger_2 f^\dagger_1$, so no need to change it. And we define $|1, 1\rangle = f^\dagger_1 f^\dagger_2 |0,0\rangle$, so $f_1 f_2 |1,1\rangle = -|0,0\rangle$.

[sanderdemeyer]

Maybe we should put this convention in the docs, like we did with Hubbard and tJ. Something similar to those cases, e.g. saying that the basis states are

    |0⟩ (vacuum), |1⟩ = (c)†|0⟩,

could be useful. Since this is a bit trivial, I'll let you decide, since it is not strictly necessary to add this for me.

[Yue-Zhengyuan]

For t-J and Hubbard we had those explanations because each fermion operator carries a label, and we have to specify which label is which state. And for Hubbard, one site can have two fermions and we need to specify whether (up, down) or (down, up) is used. For spinless fermion there's no such ambiguity for 1-site basis states. The problem we encounter here is about "many-site" states. So I think we don't need to add this line in the docs.