Transient dynamical phase diagram of the spin-boson model at finite temperature

We present numerically exact inchworm quantum Monte Carlo results for the real-time dynamics of the spin polarization in the sub-Ohmic spin-boson model. We focus in particular on the localization and coherence behavior of the model across a range of system-bath couplings, sub-Ohmic exponents, and temperatures. We show that the dynamical zero-temperature phase diagram, which is obtained from short and intermediate times, differs from the equilibrium phase diagram in both the values of critical couplings, and the associated critical exponents. We also identify and quantitatively analyze two independent mechanisms that control the loss of coherence: a smooth damping-driven crossover and a sharp frequency-driven transition. The interplay between these two decoherence mechanisms depends on the temperature of the system in a nontrivial way.