Integrability and braided tensor categories

Abstract

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.

23 pages

References in corpus (6)

• Interacting anyons in topological quantum liquids: The golden chain
• Interferometry of non-Abelian Anyons
• Topological Defects on the Lattice: Dualities and Degeneracies
• Parafermionic conformal field theory on the lattice
• Chiral SU(2)_k currents as local operators in vertex models and spin chains
• Integrability as a consequence of discrete holomorphicity: loop models

Cited by in corpus (8)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Topological aspects of the critical three-state Potts model
• Conformal field theory from lattice fermions
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and ${\mathrm{RP}}^2$ models: zero-temperature phase transition versus finite-temperature crossover
• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Support theory for Drinfeld doubles of some infinitesimal group schemes
• Les Houches Lecture Notes on Tensor Networks
• Integrability of planar-algebraic models