Universal properties of the many-body Lanczos algorithm at finite size
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911445680128000 |
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| author | Capizzi, Luca Mazza, Leonardo Murciano, Sara |
| author_facet | Capizzi, Luca Mazza, Leonardo Murciano, Sara |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17424 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal properties of the many-body Lanczos algorithm at finite size Capizzi, Luca Mazza, Leonardo Murciano, Sara Quantum Physics Statistical Mechanics High Energy Physics - Theory 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. |
| title | Universal properties of the many-body Lanczos algorithm at finite size |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.17424 |