Integrability and Braided Tensor Categories

Paul Fendley (Oxford U.)

14-Jan-2021, 15:15-17:00 (3 years ago)

Abstract: Many integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess a fractional-spin conserved current. These currents have been constructed by utilising quantum-group algebras, fermionic and parafermionic operators, and ideas from ``discrete holomorphicity''. I define them generally and naturally using a braided tensor category, a topological structure familiar from the study of knot invariants, anyons and conformal field theory. Such a current amounts to terminating a lattice topological defect, and I will touch on related work on such done with Aasen and Mong. I show how requiring a current be conserved yields simple constraints on the Boltzmann weights, and that all of the many models known to satisfy these constraints are integrable. This procedure therefore gives a linear construction for ``Baxterising'', i.e. building a solution of the Yang-Baxter equation out of topological data.

HEP - theorymathematical physicsexactly solvable and integrable systems

Audience: researchers in the topic


London Integrability Journal Club

Series comments: To register for this online seminar series please fill the form:

docs.google.com/forms/d/e/1FAIpQLSfIPJS4W5aPu5Cqqy8LoeO0bQkxBMz_5DNhb04vsSWsNz6VAQ/viewform

Announcements also on

integrability-london.weebly.com/

Organizers: Andrea CavagliĆ , Nikolay Gromov, Evgeny Sobko*, Bogdan Stefanski
*contact for this listing

Export talk to