Dynamics of the spin-boson model : a comparison of the multiple Davydov D1, D1.5, D2 Ansätze

Abstract

Accuracies of three multiple Davydov Ansätze, namely, the multi-D1, the multi-D1.5, and the multi-D2 Ansätz, in describing the population dynamics of the spin boson model, are carefully examined by a detailed comparison with numerically exact (multilayer) multiconfiguration time-dependent Hartree method. The comparison shows that these three Ansätze yield quantitatively accurate results in the adiabatic (slow bath), nonadiabatic (fast bath), as well as the intermediate regime. It is found that with an increase in the energy bias and/or spin-bath coupling, a much larger multiplicity is required for the three Ansätze to capture the correct population dynamics. The multi-D1.5 Ansatz, which combines the accuracy of the multi-D1 Ansatz and the simplicity of the multi-D2 Ansatz, outperforms the multi-D2 Ansatz. The multi-D1.5 Ansatz thus provides a numerically promising alternative to the multi-D1 Ansatz in the accurate simulation of spin-boson dynamics, especially for systems with a large number of vibrational degrees of freedom.