In Fig. , ĤnoPDM and ĤnoDSE are compared to the Rabi and JC models. This helps explain which approximations lead to the various errors in the JC Hamiltonian eigenspectrum, and provides some insight into why the JC Hamiltonian tends to outperform the Rabi Hamiltonian even though the former has more approximations. Compared to the more rigorous two-level PF Hamiltonian, the JC Hamiltonian makes three additional approximations: the neglection of DSE, the removal of PDM, and the rotating-wave approximation.