## Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra

Oleg Lychkovskiy

SciPost Phys. 10, 124 (2021) · published 1 June 2021

- doi: 10.21468/SciPostPhys.10.6.124
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### 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.

### Cited by 6

### Author / Affiliations: mappings to Contributors and Organizations

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^{1}^{2}^{3}Oleg Lychkovskiy

^{1}Московский физико-технический институт / Moscow Institute of Physics and Technology [MIPT (SU)]^{2}Skolkovo Institute of Science and Technology [Skoltech]^{3}Математический институт им. В. А. Стеклова / Steklov Mathematical Institute