  Ground state instabilities of the spin-boson model is studied in this work.
The existence of sequential ground state instabilities is shown analytically
for arbitrary detuning in the two-spin system. In this model, extra
discontinuities of concurrence(entanglement measure) are found in the finite
system, which do not appear in the on-resonant model. The above results remain
intact by including extra boson modes. Moreover, by including extra modes, it
is found that ground state entanglement can be obtained and enhanced even in
the weak coupling regime.
