Naming conventions

[sanderdemeyer]

As mentioned in pull request #3, we would like to discuss the naming conventions of the Hubbard operators.

Currently, operators like e_plusmin_up (that implement the operator $e_{1,\uparrow}^\dagger e_{2,\uparrow}$) do not give enough information on what the tensor is, since operators like $e_{1,\uparrow}^\dagger e_{2,\uparrow}^\dagger$ and $e_{1,\uparrow}^\dagger e_{2,\downarrow}^\dagger$ could also be defined in the absence of symmetries.

[sanderdemeyer]

My preference would be to redefine the operators where we fully specify what they mean, so for the examples above: e_plusmin_upup for $e_{1,\uparrow}^\dagger e_{2,\uparrow}$, e_plusplus_upup for $e_{1,\uparrow}^\dagger e_{2,\uparrow}^\dagger$ and e_plusplus_updown for $e_{1,\uparrow}^\dagger e_{2,\downarrow}^\dagger$.

[lkdvos]

Any preference for e_plusup_mindown, or e_upplus_downmin (organized by site) or do you prefer e_plusmin_updown or e_updown_plusmin (organized by modifier type)?

There's also a case to be made to be more verbose: e_plusup_e_mindown might even make sense.

Since we now are explicitly separating the namespaces, there's also no need for sticking to the e if we want something else (although I quite like the e for "electron"), so even plusup_mindown is technically possible. We could also use separate letters for the different flavors: ud_plusmin (u for up and d for down) whenever we separate, e_plusmin for the combination.

[sanderdemeyer]

I have a slight preference for either e_plusup_e_mindown or e_plusup_mindown. I like the conciseness of the latter, but it would (I think) make a bit more sense to go for the former, since we will eventually want to define things like e⁺e⁻.

[Jutho]

What is the e denoting? Is that for electron? The shortest would be to use c for creation and a for annihilation, which could give things like cꜛaꜜ. But it is maybe slightly less readable if you do not know the convention.

[sanderdemeyer]

I would also be fine with this, although I'm more used to seeing either c or a for the annihilation operator and $c^\dagger $ or $a^\dagger$ for the creation operator.

[Jutho]

Why not

(hopꜛꜛ, hopꜛꜜ, hopꜜꜛ, hopꜜꜜ) 

? 😄

[lkdvos]

We can definitely also have this, but that would already be the sum of a plusmin and minplus term, and we might want to also support the separate terms? Maybe also plusplus and minmin can be relevant in some cases