Spectral determinant of the two-photon quantum Rabi model

• URL: http://arxiv.org/abs/2206.02509v3
• Date: Wed, 3 Jan 2024 15:55:59 GMT
• Title: Spectral determinant of the two-photon quantum Rabi model
• Authors: Daniel Braak
• Abstract summary: We show that 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. We derive this function rigorously employing the $mathbbZ_4$-symmetry of the model and show that its zeros correspond to the complete regular spectrum.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. We derive this function rigorously employing the $\mathbb{Z}_4$-symmetry of the model and show that its zeros correspond to the complete regular spectrum.

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