Flexible scheme to truncate the hierarchy of pure states

The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.