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Starts to look great; this will be a very useful addition. |
| ```math | ||
| \sum_g R^{ab}_g F^{abx}_{cg} R^{ax}_c = \sum_{f,h} F^{bax}_{cf} R^{af}_h F^{axb}_{ch} | ||
| ``` | ||
| and the analogous equation with ``a`` and ``b`` swapped. |
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There's more to it than just swapping a and b, but it's probably not worth going into it. Maybe meet halfway and say something about over- and underbraiding?
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yeah, although I guess I really just need to sit down and put some actual figures together 😢
| | [`FermionNumber`](@ref) | fU₁ | Unique | Fermionic | Yes | Fermion number conservation | | ||
| | [`FermionSpin`](@ref) | fSU₂ | Simple | Fermionic | Yes | Fermions with spin symmetry | | ||
| | [`ProductSector`](@ref) | Product categories | Varies | Varies | Varies | Multiple simultaneous symmetries | | ||
| | [`TimeReversed`](@ref) | Inverted braiding | Varies | Varies | Varies | ?? | |
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Symmetries of the bra state or Drinfeld centers of modular tensor categories are what I can come up with on the spot
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I also wonder if the last column is really useful, but I guess it doesn't hurt to mention?
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I'm not even sure if this table is all that useful to begin with, but copilot generated it and I like how it looks...
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While this might look more scary, I would say the categories are Rep[SU₂] and so forth instead of simply SU₂. Or maybe something like SU₂ representations to make it more colloquial.
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Overall amazing work! The pages are pretty short, so I'm wondering if it's beneficial to have this depth to the headers? Also, do you think these docs should also mention the other packages supporting |
Co-authored-by: Boris De Vos <143942306+borisdevos@users.noreply.github.com>
| **Example: `U1Irrep`** | ||
| ```julia | ||
| # U₁ an irrep for each integer: 0, 1, -1, 2, -2, ... | ||
| Base.iterate(::SectorValues{U1Irrep}, i = 0) = (U1Irrep(i), i <= 0 ? (-i + 1) : -i - 1) |
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This is not correct even if we were to only iterate over the integer values, since the last value should be -i instead of -i-1. But the actual implementation is
function Base.iterate(::SectorValues{U1Irrep}, i::Int = 0)
return i <= 0 ? (U1Irrep(half(i)), (-i + 1)) : (U1Irrep(half(i)), -i)
endMaybe SU2Irrep is a better example:
| Base.iterate(::SectorValues{U1Irrep}, i = 0) = (U1Irrep(i), i <= 0 ? (-i + 1) : -i - 1) | |
| Base.iterate(::SectorValues{SU2Irrep}, i::Int = 0) = (SU2Irrep(half(i)), i + 1) |
Co-authored-by: Jutho <Jutho@users.noreply.github.com>
3 participants
This is ongoing work to start properly documenting this package.
It is based on the work in TensorKit, credits go to @Jutho for that.
The docs now consist of two large parts: The first part defines the interface of
Sector, while the second is a list of the concrete types provided by this package.I think the first part fixes #56 and is somewhat ready for review.
I am pretty happy with the general lay-out, but comments are obviously more than welcome.
Many of the formulas will require checking for errors, I have been doing this on the side while waiting for other PRs, so many things will have slipped my full attention.
For the second part, (related to #57) I for now only filled out the
SU2Irreppage in an attempt to show what I had in mind to document the different conventions. Before I continue with the rest (or others can chime in), I wanted to get a round of review in.