Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Quantum Monte Carlo Study with a Continuous Imaginary Time Cluster Algorithm

A continuous time cluster algorithm for two-level systems coupled to a dissipative bosonic bath is presented and applied to the sub-Ohmic spin-boson model. When the power s of the spectral function J(omega)proportional to omega(s) is smaller than 1/2, the critical exponents are found to be classical, mean-field like. Potential sources for the discrepancy with recent renormalization group predictions are traced back to the effect of a dangerously irrelevant variable.