Integrability vs exact solvability in the quantum Rabi and Dicke models

TL;DR

This paper investigates the integrability of the quantum Rabi and Dicke models, identifying specific parameter values where they are exactly solvable via Yang-Baxter integrability, contrasting with previous phenomenological claims.

Contribution

It demonstrates that the fully quantized Rabi model is Yang-Baxter integrable at specific parameters and clarifies the distinction between integrability and exact solvability in these models.

Findings

Identified Yang-Baxter integrable points in the Rabi and Dicke models

Contrasted integrability with phenomenological criteria of solvability

Implications for level statistics of the Dicke model

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.