Topological defect lines and integrability at roots of unity

par Eric Vernier

mercredi 3 juin 2026, 11:00 → 12:00 Europe/Paris

Auditorium Vivargent (LAPTh)

Topological defect lines appear in a variety of physical systems, from lattice models to field theories, with the defining property that they can be smoothly deformed without affecting physical quantities. A famous example is the defect associated with Kramers–Wannier duality in the two-dimensional Ising model, whose modern reinterpretation by Aasen Fendley and Mong has allowed to construct a general theory of topological defects in statistical mechanical systems or their quantum counterpart. Integrable lattice models provide a particularly rich setting for these ideas. In such models, the Yang–Baxter equation ensures the existence of infinitely many conserved quantities and underlies their exact solvability. At the same time, it can also be viewed as expressing a form of topological invariance on the lattice. In this talk, I will discuss these connections in the paradigmatic six-vertex (or XXZ) model, with special emphasis on its “root-of-unity” points. At these special values of the parameters, the model acquires an enhanced symmetry structure and becomes “superintegrable.” I will explain how this leads naturally to the Onsager algebra, originally introduced in Onsager’s classic solution of the Ising model, and how generalized notions of topological defect lines emerge in this setting. In particular, I will show how one can construct a duality defect closely analogous to the celebrated Ising defect.