Onsager symmetries in $U(1)$ -invariant clock models

Journal article

We show how the Onsager algebra, used in the original solution of the two-dimensional Ising model, arises as an infinite-dimensional symmetry of certain self-dual models that also have a symmetry. We describe in detail the example of nearest-neighbour n-state clock chains whose symmetry is enhanced to . As a consequence of the Onsager-algebra symmetry, the spectrum of these models possesses degeneracies with multiplicities 2 N for positive integer N. We construct the elements of the algebra explicitly from transfer matrices built from non-fundamental representations of the quantum-group algebra . We analyse the spectra further by using both the coordinate Bethe ansatz and a functional approach, and show that the degeneracies result from special exact n-string solutions of the Bethe equations. We also find a family of commuting chiral Hamiltonians that break the degeneracies and allow an integrable interpolation between ferro- and antiferromagnets.

Authors: Vernier, E; O'Brien, E; Fendley, P

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Science
• Journal: Journal of Statistical Mechanics: Theory and Experiment
• Volume: 2019
• Issue: April 2019
• Article number: 043107
• Publication date: 2019-04-30
• Acceptance date: 2019-03-05
• DOI: 10.1088/1742-5468/ab11c0
• ISSN: 1742-5468
• Language: English
• Keywords: FFR