论文标题
与Onsager代数的可集成模型中海森堡方程的封闭层次结构
Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
论文作者
论文摘要
量子系统的动力学可以通过耦合的Heisenberg方程来描述。在通用多体系统中，这些方程式形成了指数较大的层次结构，该层次结构是棘手的，没有近似值。相比之下，在一个可集成的系统中，一小部分操作员可以就哈密顿式的换向。结果，这些操作员的Heisenberg方程可以形成适合分析处理的较小的封闭系统。我们证明，这确实发生在一类可集成模型中，其中哈密顿量是Onsager代数的要素。我们明确为来自该代数的操作员的海森堡方程式解决了系统。两个特定的模型被视为示例：横向场ISING模型和可整合的手性3态POTTS模型。
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.
