  We study the ground state (GS) and excitation gap of anisotropic quantum Rabi
model (QRM) which connects the fundamental QRM and the Jaynes-Cummings model
(JCM). While the GS has a second-order quantum phase transition (QPT) in the
low frequency limit, turning on finite frequencies we shed a novel light on the
phase diagram to illuminate a fine structure of first-order transition series.
We find the QPT is accompanied with a hidden symmetry breaking, whereas the
emerging series transitions are topological transitions without symmetry
breaking. The topological structure of the wave function provides a novel
universality classification in bridging the QRM and the JCM. We show that the
conventionally established triple point is actually a quintuple or sextuple
point and following the penta-/hexa-criticality emerge a series of
tetra-criticalities.
