Comment on "Integrability of the Rabi Model"

TL;DR

This paper critiques Braak's solution to the quantum Rabi model, demonstrating that it does not encompass all eigenvalues, specifically showing that Judd's solutions are only a subset of the full spectrum.

Contribution

It reveals that Braak's solution is incomplete by identifying additional eigenvalues not captured by Judd's solutions using Hill's determinant method.

Findings

Judd's solutions form only a subset of the Rabi model's eigenvalues.

Braak's solution does not account for all eigenvalues of the Rabi model.

Additional eigenvalues are identified beyond Judd's solutions.

Abstract

Using Hill's determinant method we show that the set of Judd's solutions is only a subset of all the eigenvalues with the form $E_n=n\omega-g^2/\omega$ in the spectrum of the Rabi model. Therefore Braak's solution of the quantum Rabi model is not complete.