Theoretical study classifies rank-N spin-chain braid representations up to isomorphism, revealing algebraic structures underlying charge-conserving Yang-Baxter solutions.
A braid representation is a monoidal functor from the braid category B B , for example given by a solution to the constant Yang-Baxter equation. Given a monoidal category C C with ob(C)= N o b ( C ) = N , a rank- N charge-conserving representation, or spin-chain representation, is a strict monoidal functor F from C C to the category MatchN Match N of rank- N charge-conserving matrices (see below for definition), that is natural in the sense that $$F(1)=1$$ F ( 1 ) = 1 . In this work we construct all spin-chain braid representations, and classify up to suitable notions of isomorphism.
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Martin et al. (2026) studied this question.
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