Quantum phase transition in the sub-Ohmic spin-boson model: An extended coherent-state approach

We propose a general extended coherent state approach to the qubit (or fermion) and multimode 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.