Onsager algebra and algebraic generalization of Jordan-Wigner transformation

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 $\mathcal{H}$ as $\mathcal{H}={\sum }_{i=1}^N{J}_i{\eta }_i$, 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.

15 pages

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Cited by in corpus (1)

• Generalised Onsager Algebra in Quantum Lattice Models