Universal properties of the many-body Lanczos algorithm at finite size

• URL: http://arxiv.org/abs/2507.17424v1
• Date: Wed, 23 Jul 2025 11:31:13 GMT
• Title: Universal properties of the many-body Lanczos algorithm at finite size
• Authors: Luca Capizzi, Leonardo Mazza, Sara Murciano,
• Abstract summary: We study the universal properties of the Lanczos algorithm applied to finite-size many-body quantum systems.<n>We conjecture that in the large $n$ limit, the ratios between consecutive Lanczos coefficients should have specific scalings with the size of the lattice.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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