This analysis finds specific scalings in the ratios of Lanczos coefficients in finite-size quantum systems, suggesting new insights into hydrodynamic tails.
We study the universal properties of the Lanczos algorithm applied to finite-size many-body quantum systems. Focusing on autocorrelation functions of local operators and on their infinite-time behaviour at finite size, we conjecture that in the large n limit, the ratios between consecutive Lanczos coefficients should have specific scalings with the size of the lattice that we make precise and that depend on the hydrodynamic tail of the autocorrelation function. The scaling associated with strong or approximate zero-modes is also discussed. We support our conjecture with a numerical study of different models.
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Capizzi et al. (2025) studied this question.
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