Comment on "Integrability of the Rabi model"

In his recent letter, Braak suggested that a regular spectrum of the Rabi model was given by the zeros of a transcendental function $G_{\pm }(x)$ (cf Eqs. (3)-(5) of Ref. [1]) and highlighted the role of the discrete ${\mathbb{Z}}_2$-symmetry, or parity, in determining $G_{\pm }(x)$. We show here to the contrary that one can define a transcendental function $F_0(x)$ and obtain the regular spectrum of the Rabi model as the zeros of $F_0(x)$ (see Fig. 1) without ever making use of the underlying ${\mathbb{Z}}_2$-symmetry of the model.