The real-time renormalization group approach for the spin-boson model in nonequilibrium

We investigate the dynamics of the spin-boson model with ohmic dissipation. We use a real-time renormalization group method by which we are able to study the nonequilibrium problem. The full time evolution of the reduced density matrix is calculated. The asymptotic behaviour is given by an exponential decay characterized by the relaxation and the dephasing time. These parameters are determined from the results for the reduced density matrix. Furthermore we calculate the static susceptibility and equilibrium correlation functions. We compare our results both with quantum Monte Carlo calculations and with results obtained for the Kondo model. The Shiba-relation is confirmed within our approach. The correct relaxation behaviour both for long and short to intermediate time scales is found for the whole parameter region with the only restriction of not too large coupling strength. (C) 2001 Elsevier Science B.V. All rights reserved.