Transient dynamical phase diagram of the spin–boson model

We obtain the real-time dynamics of the sub-Ohmic spin–boson model using the numerically exact inchworm Quantum Monte Carlo algorithm. From short- and intermediate-time dynamics starting from an initially decoupled state, we extract signatures of the zero-temperature quantum phase transition between localized and delocalized states. We show that the dynamical phase diagram thus obtained 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 competing mechanisms for the crossover between coherent oscillations and incoherent decay. Deep in the sub-Ohmic regime, the crossover is driven by the damping of the oscillation amplitude, while closer to the Ohmic regime the oscillation frequency itself tends to zero at large coupling. The inchworm algorithm is efficient over a wide range of temperatures and thus allows us to examine the changes in dynamics as the temperature is increased above zero.