Characterize the generality and origin of early large‑m correlations in block Lanczos

Ascertain whether the earlier onset of strong correlations between large‑iteration block Lanczos energy estimators, compared to scalar Lanczos, is a generic phenomenon across datasets and determine which algorithmic features (such as loss of biorthogonality after convergence of particular Ritz vectors) are responsible for these differences.

Background

The authors observe that bootstrap‑median energy estimators from block Lanczos exhibit strong correlations at smaller iteration counts than scalar Lanczos in their nucleon example, hinting at potentially faster convergence characteristics.

They explicitly state that, based on this single example, it is not clear whether this behavior is generic or which aspects of the Lanczos process cause it, pointing to a need for systematic investigation of the phenomenon and its mechanism.