  The Dirac-Frenkel time-dependent variational approach with Davydov Ans\"atze
is a sophisticated, yet efficient technique to obtain an acuurate solution to
many-body Schr\"odinger equations for energy and charge transfer dy- namics in
molecular aggregates and light-harvesting complexes. We extend this variational
approach to finite temperatures dynamics of the spin-boson model by adopting a
Monte Carlo importance sampling method. In or- der to demonstrate the
applicability of this approach, we compare real-time quantum dynamics of the
spin-boson model calculated with that from numerically exact iterative
quasiadiabatic propagator path integral (QUAPI) technique. The comparison shows
that our variational approach with the single Davydov Ans\"atze is in excellent
agreement with the QUAPI method at high temperatures, while the two differ at
low temperatures. Accuracy in dynamics calculations employing a multitude of
Davydov trial states is found to improve substantially over the single Davydov
Ansatz, especially at low temperatures. At a moderate computational cost, our
variational approach with the multiple Davydov Ansatz is shown to provide
accurate spin-boson dynamics over a wide range of temperatures and bath
spectral densities.
