where C eff (t) is the effective TCF according to bosonic fluctuation-dissipation theorem. Unfortunately, we do not have a closed analytic form for F -1 [κ(ω)]. Nevertheless, one can still evaluate it numerically. Being in line with the HEOM formalism (see Sec. I of the Supplementary Material), if we assume that the effective TCF can be decomposed into a series of exponential decay basis, which means