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Lanczos, the transfer matrix, and the signal-to-noise problem

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arxiv 2406.20009 v4 pith:MUCVRF3Z submitted 2024-06-28 hep-lat hep-phnucl-th

Michael L. Wagman This is my paper · ORCID
classification hep-lathep-phnucl-th
keywords lanczosmethodalgorithmenergylqcdmassmatrixprovides
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This work introduces a method for determining the energy spectrum of lattice quantum chromodynamics (LQCD) 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 LQCD 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 multi-state 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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Lattice evidence that scalar glueballs are small

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    hep-lat 2026-07 conditional novelty 7.0 of 10

    First lattice-QCD constraints on the nonperturbative gluon Collins-Soper kernel are obtained at near-physical pion mass with uNNLL LaMET matching on a single a=0.15 fm ensemble.

  3. Unbiased Krylov subspace method for the extraction of ground state from lattice correlators

    hep-lat 2025-11 unverdicted novelty 6.0 of 10

    SVD low-rank approximation plus variance extrapolation removes bias from Krylov subspace ground-state extraction in lattice correlators.

  4. Lattice QCD Study of Positive Parity Dibaryons with Maximal Charm and Strangeness

    hep-lat 2025-07 conditional novelty 6.0 of 10

    Lattice QCD finds the Omega_ccc-Omega_ccc dibaryon likely bound by about 45 MeV in the spin-0 channel, Omega-Omega near threshold, and both spin-2 systems unbound.

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