In contrast, for simplified model Hamiltonians, it is often possible to construct exact closed-form expressions of the second, third, and higher order cumulants. Additionally, higher order cumulants for model systems can be constructed numerically. These model systems can provide powerful insights into the types of errors made in evaluating low-order cumulant expansions using QCFs. In this work, we focus on the GBOM Hamiltonian 39 (see Sec. A 1), for which analytical expressions for g 2 (t) and g 3 (t) based on quantum and classical correlation functions and QCFs, as well as the exact result corresponding to the infinite order cumulant expansion can be computed analytically (see SI Sec. I and Ref. 39).