Spectral Determinant of the Two‐Photon Quantum Rabi Model

Abstract

The various generalized spectral determinants (G-functions) of the two-photon quantum Rabi model are analyzed with emphasis on the qualitative aspects of the regular spectrum. Whereas all of them yield at least a subset of the exact regular eigenvalues, only the G-function proposed by Chen et al. in 2012 exhibits an explicitly known pole structure which dictates the approach to the collapse point. This function is derived rigorously employing the ℤ 4 -symmetry of the model and shown that its zeros correspond to the complete regular spectrum.