Onsager algebra and algebraic generalization of Jordan-Wigner transformation

TL;DR

This paper shows that operators derived from a generalized Jordan-Wigner transformation generate the Onsager algebra, linking algebraic structures to integrable models and extending the transformation's applicability.

Contribution

It demonstrates that operators from the algebraic generalization of Jordan-Wigner transformation generate the Onsager algebra, revealing new algebraic connections in integrable systems.

Findings

Operators generate the Onsager algebra

Connection to integrable models established

Extension to n-state clock generalizations

Abstract

Recently, an algebraic generalization of the Jordan-Wigner transformation was introduced and applied to one- and two-dimensional systems. This transformation is composed of the interactions $\eta_{i}$ that appear in the Hamiltonian ${\cal H}$ as ${\cal H}=\sum_{i=1}^{N}J_{i}\eta_{i}$, where $J_{i}$ are coupling constants. In this short note, it is derived that operators that are composed of $\eta_{i}$, or its $n$-state clock generalizations, generate the Onsager algebra, which was introduced in the original solution of the rectangular Ising model, and appears in some integrable models.