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SUMMARY:Topological defect lines and integrability at roots of unity
DTSTART:20260603T090000Z
DTEND:20260603T100000Z
DTSTAMP:20260602T124900Z
UID:indico-event-38045@indico.in2p3.fr
CONTACT:seminars@lapth.cnrs.fr
DESCRIPTION:Speakers: Eric Vernier\n\nTopological defect lines appear in a
  variety of physical systems\, from lattice models to field theories\, wit
 h the defining property that they can be smoothly deformed without affecti
 ng physical quantities. A famous example is the defect associated with Kra
 mers–Wannier duality in the two-dimensional Ising model\, whose modern r
 einterpretation by Aasen Fendley and Mong has allowed to construct a gener
 al theory of topological defects in statistical mechanical systems or thei
 r quantum counterpart. Integrable lattice models provide a particularly r
 ich setting for these ideas. In such models\, the Yang–Baxter equation e
 nsures the existence of infinitely many conserved quantities and underlies
  their exact solvability. At the same time\, it can also be viewed as expr
 essing a form of topological invariance on the lattice.In this talk\, I wi
 ll discuss these connections in the paradigmatic six-vertex (or XXZ) model
 \, with special emphasis on its “root-of-unity” points. At these speci
 al values of the parameters\, the model acquires an enhanced symmetry stru
 cture and becomes “superintegrable.” I will explain how this leads nat
 urally to the Onsager algebra\, originally introduced in Onsager’s class
 ic solution of the Ising model\, and how generalized notions of topologica
 l 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.\n\nhttps://indico.in2p3.fr/event/38045/
LOCATION:Auditorium Vivargent (LAPTh)
URL:https://indico.in2p3.fr/event/38045/
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