Kavli Affiliate: Masahito Yamazaki
| Summary:
We establish a direct connection between Onsager symmetry, duality defects, and quantum integrability in the XXZ spin chain at roots of unity, $Δ=(q+q^-1)/2$ with $q^N=pm1$. Using a non-Abelian algebra of transfer matrices governed by an unbalanced version of the Yang–Baxter/RLL relation, we construct an explicit lattice realization of the Onsager algebra and its duality automorphism. The duality is represented by a matrix product operator related to the transfer matrices of the $τ_2$ model. We show that this operator obeys $mathbbZ_N$ Tambara–Yamagami fusion rules and therefore realizes on the lattice the topological defect lines of the free compactified boson conformal field theory. Our results identify non-Abelian integrability as a natural framework for the emergence of the Onsager symmetry and categorical dualities in lattice models.
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