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[Sectors] Non-abelian fusion #1363

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@ogauthe ogauthe commented Mar 25, 2024

This is a work in progress for a full implementation of non-abelian fusion rules in Sectors. It also contains several patches on other components of Sectors. A core aspect is that the dependency order between GradedAxes and Sectors has been reversed: Sectors now depends on GradedAxes.

To do:

  • implement fusion rules for CategoryProduct
  • implement SymmetryStyle trait with values AbelianGroup, NonAbelianGroup and NonGroupSymmetry

To be decided:

  • type return for c1 ⊗ c2: either always a GradedUnitRange or a GradedUnitRange or a Category depending on SymmetryStyle
  • whether to keep SU2 and SU{2}.
  • whether to implement SU(N) fusion rules or add dependency / fork SUNRepresentations.jl

Decisions:

  • c1 ⊗ c2: return type depends on SymmetryStyle
  • work on replacing SU2 with SU{2} and try to have a half-integer interface specific to SU{2}

Long term: how to handle braiding for fermions and anyons.

rebase on latest GradedAxes
set GradedAxes as a Sector dependency
define fusion rules for simple categories
pass test for simple categories
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codecov-commenter commented Mar 25, 2024

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 57.49%. Comparing base (ceb26a7) to head (1fa1f7b).

❗ Current head 1fa1f7b differs from pull request most recent head de95045. Consider uploading reports for the commit de95045 to get more accurate results

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Additional details and impacted files
@@            Coverage Diff             @@
##             main    #1363      +/-   ##
==========================================
+ Coverage   49.23%   57.49%   +8.26%     
==========================================
  Files         110      114       +4     
  Lines        8320     8867     +547     
==========================================
+ Hits         4096     5098    +1002     
+ Misses       4224     3769     -455     

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@emstoudenmire
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Regarding the question of the SU(2) types, I believe we had settled on the following plan

  • remove the specialized SU(2) type and just have a single type for all SU(N)
  • add a type parameter which sets the convention of using integer versus half-integer labels (though does this concept generalize to SU(N) well?)
  • specialize certain methods to the SU{2} case whenever performance is a concern. Though at first maybe don't do this at all and just check later by profiling if this is an issue.

@ogauthe ogauthe marked this pull request as draft June 18, 2024 16:17
Comment on lines +9 to +10
gradedisequal(::AbstractUnitRange, ::OneToOne) = false
gradedisequal(::OneToOne, ::AbstractUnitRange) = false
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Shouldn't these be true if the AbstractUnitRange runs from 1:1 and doesn't have any labels?

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4 participants