Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra

Abstract

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.

arXiv commentSubmission to SciPost

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• Duality between open systems and closed bilayer systems: Thermofield double states as quantum many-body scars
• Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Effect of dephasing on the current through a periodically driven quantum point contact
• Polynomially restricted operator growth in dynamically integrable models
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra
• Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies