Integrability and braided tensor categories

Journal article

Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on the Boltzmann weights admitting a conserved current, generalising one found using quantum-group algebras. The resulting trigonometric weights are typically those of a critical integrable lattice model, so the method here gives a linear way of “Baxterising”, i.e. building a solution of the Yang-Baxter equation out of topological data. It also illuminates why many models do not admit a solution. I discuss many examples in geometric and local models, including (perhaps) a new solution.

Authors: Fendley, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Journal of Statistical Physics
• Volume: 182
• Issue: 2
• Article number: 43
• Publication date: 2021-02-18
• Acceptance date: 2021-01-20
• DOI: 10.1007/s10955-021-02712-6
• EISSN: 1572-9613
• ISSN: 0022-4715
• Language: English
• Keywords: knot and link invariants; Yang-Baxter equation; integrability; tensor categories; FFR