Identify the optimal cluster choice

Determine the optimal number and composition of clusters for cluster mean field and cluster perturbation calculations, balancing accuracy against the increased computational cost of larger clusters.

Background

The paper compares alternative cluster partitions for pyrene and coronene. Larger clusters improve the cluster mean-field energy substantially, but the corresponding gains at second-order cluster perturbation theory are smaller, while larger clusters increase the number of cluster states and the cost of correlated calculations.

The authors therefore leave unresolved which cluster size and partitioning provide the best overall accuracy-cost balance. This question is central to applying cluster methods to systems with multiple resonance structures and nonlocal correlations.

References

Considering that using larger clusters can increase the cost of correlated calculations, it remains to be seen what the optimal cluster choice is.

— Examination of Cluster Based Methods to Fermionic Systems  (2609.08773 - Keyes et al., 8 Sep 2026) in Section 5, Results and Discussion, paragraph following Tables 5 and 6

Their optimization, together with optimal certificate cluster selection, is left for future work.

— Structured Positive-Definite Optimal Control Synthesis of Closed-Loop Recommendation Systems over Social Networks  (2609.08567 - Simone et al., 8 Sep 2026) in Remark 2.14, Section 5.1 (Local-to-global dissipativity-based design)