Generalised Onsager Algebra in Quantum Lattice Models

• URL: http://arxiv.org/abs/2203.16594v4
• Date: Wed, 17 Aug 2022 10:58:06 GMT
• Title: Generalised Onsager Algebra in Quantum Lattice Models
• Authors: Yuan Miao
• Abstract summary: The Onsager algebra is one of the cornerstones of exactly solvable models in statistical mechanics. We demonstrate its relations to the graph Temperley-Lieb algebra, and a generalisation of the Onsager algebra. We present a series of quantum lattice models as representations of the generalised Clifford algebra.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Onsager algebra is one of the cornerstones of exactly solvable models in statistical mechanics. Starting from the generalised Clifford algebra, we demonstrate its relations to the graph Temperley-Lieb algebra, and a generalisation of the Onsager algebra. We present a series of quantum lattice models as representations of the generalised Clifford algebra, possessing the structure of a special type of the generalised Onsager algebra. The integrability of those models is presented, analogous to the free fermionic eight-vertex model. We also mention further extensions of the models and physical properties related to the generalised Onsager algebras, hinting at a general framework that includes families of quantum lattice models possessing the structure of the generalised Onsager algebras.

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