which is the absolute [ value]{} of $\langle \sigma _{z}\rangle $ in our paper. In the weak-coupling limit, $\langle \sigma _{z}\rangle $ is actually $-1$ as stated above. In the strong-coupling limit, we always [ find]{} $\langle
\sigma _{z}\rangle >0$ in the ground-state, so, [ in between]{} $\langle
\sigma _{z}\rangle $ must cross zero, resulting in the drop of $\left\vert
\langle \sigma _{z}\rangle \right\vert $ to zero at some coupling that is not at any phase transition point. $\left\vert
\langle \sigma _{x}\rangle \right\vert $ is the order parameter of the second-order QPT, so it only becomes non-zero for couplings larger than the critical one.

[ ]{}In short, we find rich phase transitions in the sub-Ohmic spin-boson model with the RWA. First,  the second-order QPT occurs for any finite model parameters, similar to its counterpart without the RWA. In both the Rabi model and the Dicke model with the RWA, the second-order QPTs cannot happen for finite ratio $\Delta /\omega $  or finite qubit number. Second, for larger bath exponents, e.g., $s=$ $0.7$, both the first- and second-order QPTs occur subsequently with the coupling strength. Several first-order phase transitions before the critical points indicate a sequence of instabilities. The first-order phase 