On the Existence of Monodromies for the Rabi model

We discuss the existence of monodromies associated with the singular points of the eigenvalue problem for the Rabi model. The complete control of the full monodromy data requires the taming of the Stokes phenomenon associated with the unique irregular singular point. The monodromy data, in particular the composite monodromy, are written in terms of the parameters of the model via the isomonodromy method and the tau-function of the Painlev\'e V. These data provide a systematic way to obtain the quantized spectrum of the Rabi model.