As mentioned above, the number of imaginary time evolution steps 𝑁𝑁 𝑖𝑖𝑖𝑖𝑎𝑎𝑖𝑖 , the size of bond dimension 𝐷𝐷, the size of local phonon basis 𝑑𝑑 𝐻𝐻 , the size of real time evolution step Δ𝑡𝑡 and the number of sites 𝑁𝑁 are essential parameters to assure the accuracy of calculations. In this work, we focus on the challenging intermediate parameter regime where 𝜏𝜏 is comparable to 𝜆𝜆 and room temperature. In Supporting Information 3, we demonstrate that in this case, the converged and valid results can be obtained by TD-DMRG with a moderate computational cost. For most of the parameter regimes we are interested in, parameter set of Δ𝑡𝑡 = 50, 𝑁𝑁 = 12, 𝐷𝐷 = 48 and 𝑑𝑑 𝐻𝐻 = 9 is enough for numerical convergence.