2020/08/05 by Paul Fendley
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Conformal map #Integrable system #Ising model #Knot (papermaking) #Knot theory #Lattice (music) #Quantum many-body systems #Simple (philosophy) #Tensor (intrinsic definition) #Trigonometry #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/s10955-021-02712-6
published as J Stat Phys 182, 43 (2021) · 23 pages
arxiv created 2020/08/05 · openalex created_date 2020/08/10 · openalex publication_date 2021/02/01 · arxiv updated 2021/03/10 · openalex updated_date 2026/08/05
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.