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Dynamics of the sub-Ohmic spin-boson model is investigated by employing amultitude of the Davydov D$_1$ trial states, also known as the multi-D$_1$Ansatz. Accuracy in dynamics simulations is improved significantly over thesingle D$_1$ Ansatz, especially in the weak system-bath coupling regime. Thereliability of the multi-D$_1$ Ansatz for various coupling strengths andinitial conditions are also systematically examined, with results comparedclosely with those of the hierarchy equations of motion and the path integralMonte Carlo approaches. In addition, a coherent-incoherent phase crossover inthe nonequilibrium dynamics is studied through the multi-D$_1$ Ansatz. Thephase diagram is obtained with a critical point $s_{c}=0.4$. For $s_{c}<s<1$,the coherent-to-incoherent crossover occurs at a certain coupling strength,while the coherent state recurs at a much larger coupling strength. For$s<s_{c}$, only the coherent phase exists.

Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov $\mathrm{D}_1$ states