  The experimental advance on light-matter interaction into strong couplings
has invalidated Jaynes-Cummings model and brought quantum Rabi model (QRM) to
more relevance. The QRM only involves linear coupling via a single-photon
process (SPP), while nonlinear two-photon process (TPP) is weaker and
conventionally neglected. However, we find a contrary trend that enhancing the
linear coupling might not suppress more the nonlinear effect but backfire to
trigger some collapse of linear characters. Indeed, in strong SPP couplings a
tiny strength of TPP may dramatically change properties of the system, like a
symmetry spontaneous breaking. By extracting the ground-state phase diagram
including both SPP and TPP, we find TPP in low frequency limit induces a
quantum phase transition with continuity-discontinuity double faces, which
split into two distinct transitions at finite frequencies and yields a triple
point. Our analysis unveils a subtle SPP-TPP entanglement.
