Finite-temperature time-dependent variation with multiple Davydov states

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.