Cumulant reduced density matrices as measures of statistical dependence and entanglement between electronic quantum domains with application to photosynthetic light harvesting

Recent ultrafast spectroscopy experiments have demonstrated the entanglement of chromophores in photosynthetic light harvesting. Here we apply the cumulant parts of reduced density matrices (RDMs) to measure the statistical dependence and entanglement between electronic quantum domains in light harvesting. Because the cumulant RDMs are invariant to one-electron unitary transformations, they provide a measure of electron correlation and entanglement that is independent of the orbital basis set. Specifically, we apply the cumulant to a three-chromophore subsystem of the Fenna-Matthews-Olson complex, which has been shown to exhibit similar entanglement as the full system. Time-dependent Frobenius norms of the cumulant p-RDMs for 2 <= p <= 6 reveal correlation and entanglement in groupings of p chromophores. The results show that the entanglement of pairs of chromophores is significantly more important than the entanglement in higher groupings of the chromophores. Data from the model are generally consistent with recent findings from ultrafast spectroscopy. Beyond their application to light harvesting, the Frobenius norms of the cumulant RDMs provide a useful measure of statistical dependence, correlation, and entanglement between electronic quantum domains with applications to molecules and materials.