  Quantum Rabi model (QRM) is fascinating not only because of its broad
relevance and but also due to its few-body quantum phase transition. In
practice both the bias and the nonlinear coupling in QRM are important
controlling parameters in experimental setups. We study the interplay of the
bias and the nonlinear interaction with the linear coupling in the ground state
which exhibits various patterns of symmetry breaking and different orders of
transitions. Several situations of tricriticality are unveiled in the low
frequency limit and at finite frequencies. We find that the full
quantum-mechanical effect leads to novel transitions, tricriticalities and
quadruple points, which are much beyond the semiclassical picture. We clarify
the underlying mechanisms by analyzing the energy competitions and the
essential changeovers of the quantum states, which enables us to extract most
analytic phase boundaries.
