Abstract

Many integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess an unusual sort of conserved current. Such 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 structure familiar from the study of knot invariants and from conformal field theory.  Requiring the existence of the currents provides a simple way of ``Baxterising'', i.e. building a solution of the Yang-Baxter equation out of topological data.  This approach allows many new examples of conserved currents to be found, for example in height models.  Although integrable models found by this construction are critical, I find one non-critical generalisation: requiring a ``shift'' operator in the chiral clock chain yields precisely the Hamiltonian of the integrable chiral Potts chain.