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Comment on "Solvability of the two-photon Rabi Hamiltonian"

An implicit formula for the spectrum of the two-photon Rabi model was presented by Travenec in Phys. Rev. A 85, 043805 (2012) in analogy to the method of Braak [Phys. Rev. Lett. 107, 100401 (2011)]. The spectrum is given by common zeros of four functions $G_c(z, E)$ taken with a fixed value of $z\in\mathbb{C}$. We point out that all the $G_c(z,E)$ functions defined by Travenec are identically zero, thus the spectrum is not in fact given by their roots.