Integrable boundary conditions in the antiferromagnetic Potts model

• Published in: The journal of high energy physics Vol. 2020; no. 5; pp. 1 - 35
• Main Authors: Robertson, Niall F., Pawelkiewicz, Michal, Jacobsen, Jesper Lykke, Saleur, Hubert
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2020; Springer Nature B.V; Springer; SpringerOpen
• Subjects: Antiferromagnetism; Bethe Ansatz; Boundary conditions; Classical and Quantum Gravitation; Conformal Field Theory; Elementary Particles; Free boundaries; General Physics; High energy physics; Lattice Integrable Models; Lie groups; Mapping; Mathematical Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Lattice Integrable Models; Conformal Field Theory; Bethe Ansatz; boundary condition; algebra: Lie; model: integrability; Potts model; staggered; affine; model: vertex; algebra: Temperley-Lieb; twist; K-matrix
• ISSN: 1029-8479; 1126-6708; 1029-8479
• DOI: 10.1007/JHEP05(2020)144

A bstract We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine D 2 2 Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic Potts model, this mapping allows us to study the latter model using tools from integrability. We show that there is a simple interpretation of one of the known K -matrices of the D 2 2 model in terms of Temperley-Lieb algebra generators, and use this to present an integrable Hamiltonian that turns out to be in the same universality class as the antiferromagnetic Potts model with free boundary conditions. The intriguing degeneracies in the spectrum observed in related works ([12, 13]) are discussed.