Dynamics of the spin-boson model: the effect of bath initial conditions

Dynamics of the (sub-)Ohmic spin-boson model under various bath initial conditions is investigated by employing the Dirac-Frenkel time-dependent variational approach with the multiple Davydov ${\mathrm{D}}_1$ ansatz in the interaction picture. The validity of our approach is carefully checked by comparing results with those of the hierarchy equations of motion method. By analyzing the features of nonequilibrium dynamics, we identify the phase diagrams for different bath initial conditions. We find that for spectral exponent $s<s_c$, there exists a transition from coherent to quasicoherent dynamics with increasing the coupling strengths. For $s_c<s\le 1$, the coherent to incoherent crossover occurs at a certain coupling strength, and the quasicoherent dynamics emerges at much larger couplings. The initial preparation of the bath has considerable influence on the dynamics.