Dynamical properties of the spin-boson model using real-time quantum Monte Carlo

The spin-boson model consists of a two-state system coupled to a bath of non-interacting harmonic modes. We obtain the real-time dynamics of the population difference between the two states using the inchworm Monte Carlo algorithm. We focus on sub-Ohmic spectral densities of the bosonic bath, where the system exhibits a second order quantum phase transition between localized and delocalized regimes, as well as a crossover between coherent and incoherent dynamics. The inchworm algorithm is efficient over a wide range of temperatures (including low, intermediate, and high temperatures) and thus allows us to examine the changes in dynamics as the temperature is increased above zero. We use this to study the quantum critical behavior at finite temperature and the emergence of a quantum critical fan. We also identify and analyze two competing mechanisms for the coherent-incoherent crossover and study their temperature-dependence.