Multiple ground-state instabilities in the anisotropic quantum Rabi model

In this work, the anisotropic variant of quantum Rabi model with different coupling strengths rotating and counterrotating wave terms is studied by Bogoliubov operator approach. The anisotropy preserves parity symmetry original model. We derive corresponding $G$-function, which yields both regular exceptional eigenvalues. eigenvalues correspond to crossing points two energy levels parities, they are doubly degenerate. find analytically that ground state first excited can cross several times, indicating multiple first-order phase transitions as a function strength. These related manifest Hamiltonian, in contrast level crossings asymmetric model, caused hidden symmetry.