Lanczos Algorithm, the Transfer Matrix, and the Signal-to-Noise Problem

Wagman, Michael L.

doi:10.1103/pcvc-734h

Lanczos Algorithm, the Transfer Matrix, and the Signal-to-Noise Problem

Journal Article · Tue Jun 17 00:00:00 EDT 2025 · Physical Review Letters

DOI:https://doi.org/10.1103/pcvc-734h· OSTI ID:2407106

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Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

This Letter introduces a method for determining the energy spectrum of lattice quantum chromodynamics by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to filter out spurious eigenvalues. Proof-of-principle analyses of the simple harmonic oscillator and the lattice quantum chromodynamics proton mass demonstrate that this method provides faster ground-state convergence than the “effective mass,” which is related to the power-iteration algorithm. Lanczos provides more accurate energy estimates than multistate fits to correlation functions with small imaginary times while achieving comparable statistical precision. Two-sided error bounds are computed for Lanczos results and guarantee that excited-state effects cannot shift Lanczos results far outside their statistical uncertainties.

View Accepted Manuscript (DOE)

Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: 89243024CSC000002

OSTI ID:: 2407106

Report Number(s):: FERMILAB-PUB--24-0320-T; arXiv:2406.20009; oai:inspirehep.net:2803123

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 24 Vol. 134; ISSN 1079-7114; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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