Decision on the naming of the Hubbard operators

[sanderdemeyer]

This poll is meant to choose a specific naming convention for the Hubbard operators, as mentioned in #6. Note that these operators will for now only be used internally, and we will most likely only export certain operators in their symbolic form (like e⁺e⁻ for example). Feel free to add other options.

[lkdvos]

I wouldn't say that we only export the symbolic forms, I would rather say that this is a lower-level package that the front-end probably would not interact with directly...
As a summary:

• e_$(operatortype)$(particletype)_..., for example e_plusup_mindown
• e_$(particletype)$(operatortype)_..., for example e_upplus_downmin
• e_$(operatortypes...)_$(particletypes...)_, for example e_plusmin_updown
• e_$(particletypes...)_$(operatortypes...)_, for example e_updown_plusmin
• e_$(operatortype)$(particletype)_e_..., for example e_plusup_e_mindown
• e_$(particletype)$(operatortype)_e_..., for example e_upplus_e_downmin
• $(particletype...)_$(operatortype...), for example ud_plusmin
• $(Particletype)$(operatortype)_, for example Uplus_Dmin
• $(particletype)_$(operatortype)_..., for example u_plus_d_min

[lkdvos]

(last option not in list because the list is too long...)

[Jutho]

I have not really followed this, but where does the e come from? Is that for electron? It feels kind of redundant if you already have up and down in the name. Out of curiosity, is that a convention that was picked up from somewhere? I guess most of the physics literature uses c or a for the actual creation and annihilation operators? Personally, e+ and e- makes me think of electrons and positrons (as in QED scattering processes), so I would vote for one of the last two options.

[lkdvos]

The e did come from the namespace problem of already having used c for the spinless fermions, so I just went up the alphabet and liked e for electron. Given that here we don't have this, I agree there's no real reason to keep it. I do like having different letters for the different flavors of particles though, that sounds reasonable to me

[lkdvos]

We have decided on the following function names for the tensors:

• $particleflavour_$operatortype for single-body operators
• $particleflavour_$operatortype_$particleflavour_$operatortype for two-body operators
• ...

Here particleflavour is used to denote the type of particle, a for bosons and c for fermions, and when applicable u for spin-up fermions and d for spin-down fermions.
Similarly operatortype is used to denote the type of operator, plus for creation and min for annihilation operators and num for the number operator.

Additionally, for operators that act on spin degrees of freedom, we'll have S_$operatortype where the operatortype can be x, y, z, plus, min, etc.

For example:

c_num = c_plus_c_min
u_plus_d_min + d_plus_u_min == c_plus_c_min # hubbard case
# ...

As an aside, users could always rename things to match their own conventions:

using TensorKitTensors: c_num as number_operator
# ...