Parsing correlation functions to simplify spectroscopic simulations

Nonlinear optical signals encode rich many-body dynamics but are notoriously expensive to simulate because they depend on third-order response functions across multiple Liouville-space pathways. I will present a formally exact framework that exploits the structure of these pathways including ground-state bleach (GSB), stimulated emission (SE), and excited-state absorption (ESA), to achieve size-invariant (O(1)) scaling for two-dimensional electronic spectroscopy. The central idea is an excitation-operator decomposition that partitions the system into spatial "clusters" on the bra/ket states. In physically relevant regimes, long waiting time, strong optical dephasing, or suppressed inter-cluster correlations, key third-order contributions factorize into products of simpler first-order processes. We integrate these decompositions with the Dyadic-adaptive Hierarchy of Pure States (Dyadic-adHOPS) to retain formal exactness while removing the usual catastrophic scaling with system size. The poster will cover the rephasing/non-rephasing formulations, show how cluster sets are constructed and validated, and highlight double-sided Feynman-diagram views that make the simplifications transparent. This approach delivers both physical insight by isolating dominant local pathways and practical performance for simulating mesoscale excitonic aggregates.