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arXiv · 1408.3816

Integrability vs exact solvability in the quantum Rabi and Dicke models

Murray T. Batchelor·Huan-Qiang Zhou
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Abstract

The Rabi model describes the simplest interaction between light and matter via a two-level quantum system interacting with a bosonic field. We demonstrate that the fully quantised version of the Rabi model is integrable in the Yang-Baxter sense at two parameter values. The model is argued to be not Yang-Baxter integrable in general. This is in contrast to the claim that the quantum Rabi model is integrable based on a phenomenological criterion of quantum integrability not presupposing the existence of a set of commuting operators. Similar Yang-Baxter integrable points are identified for the generalised Rabi model and the fully quantised Dicke model. The integrable points have particular implications for the level statistics of the Dicke model.

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Murray T. Batchelor, Huan-Qiang Zhou. 2015-01-05. Integrability vs exact solvability in the quantum Rabi and Dicke models. https://doi.org/10.1103/physreva.91.053808

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