Dynamics of a quantum system can be described by coupled Heisenberg equations. In a generic many-body system these equations form an exponentially large hierarchy that is intractable without approximations. In contrast, in an integrable system a small subset of operators can be closed with respect to commutation with the Hamiltonian. As a result, the Heisenberg equations for these operators can form a smaller closed system amenable to an analytical treatment. We demonstrate that this indeed happens in a class of integrable models where the Hamiltonian is an element of the Onsager algebra. We explicitly solve the system of Heisenberg equations for operators from this algebra. Two specific models are considered as examples: the transverse field Ising model and the superintegrable chiral 3-state Potts model.

中文翻译：

---

具有 Onsager 代数的可积模型中海森堡方程的封闭层次结构

量子系统的动力学可以通过耦合的海森堡方程来描述。在一个通用的多体系统中，这些方程形成一个指数级大的层次结构，如果没有近似值就很难处理。相比之下，在可积系统中，一小部分算子在与哈密顿量的对易方面是封闭的。因此，这些算子的海森堡方程可以形成一个更小的封闭系统，可以进行分析处理。我们证明这确实发生在一类可积模型中，其中哈密顿量是 Onsager 代数的一个元素。我们从这个代数中明确地求解了海森堡方程组的算子。考虑两个特定模型作为示例：横向场 Ising 模型和超可积手性三态 Potts 模型。