From coherent motion to localization: II. Dynamics of the spin-boson model with sub-Ohmic spectral density at zero temperature

Abstract

The dynamics of the spin-boson model at zero temperature is studied for a bath characterized by a sub-Ohmic spectral density. Using the numerically exact multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method, the population dynamics of the two-level subsystem has been investigated in a broad range of parameter space. The results show the transition of the dynamics from weakly damped coherent motion to localization upon increase of the system–bath coupling strength. Comparison of the exact ML-MCTDH simulations with the non-interacting blip approximation (NIBA) shows that the latter performs rather poorly in the weak coupling regime with small Kondo parameters. However, NIBA improves significantly upon increase in the coupling strength and is quantitatively correct in the strong coupling, nonadiabatic limit. The transition from coherent motion to localization as a function of the different parameters of the model is analyzed in some detail.