  We propose a general extended coherent state approach to the qubit (or
fermion) and multi-mode boson coupling systems. The application to the
spin-boson model with the discretization of a bosonic bath with arbitrary
continuous spectral density is described in detail, and very accurate solutions
can be obtained. The quantum phase transition in the nontrivial sub-Ohmic case
can be located by the fidelity and the order-parameter critical exponents for
the bath exponents $s<1/2$ can be correctly given by the fidelity
susceptibility, demonstrating the strength of the approach.
