As shown in Fig. (c), the removal of PDM leads to an increase in the splitting at the various avoided crossings. Then, removing the DSE (in panel (d)) causes a uniform, R-dependent downward shift for all states. The combination of these approximations gives the Rabi model, as seen in panel (a). The JC model comes from applying the RWA on the Rabi model. By comparing panels (a) and (b), we see that the RWA cancels some of the errors induced by neglecting the DSE. Due to this partial cancellation of errors, the JC model indeed provides more accurate eigenspectra than the Rabi model in many cases.