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Unbiased Krylov subspace method for the extraction of ground states from lattice correlators

Ryutaro Tsuji*, Shoji Hashimoto, and Ryan Kellermann

  • *Contact author: rtsuji@post.kek.jp
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Phys. Rev. D 113, 054514 – Published 31 March, 2026

DOI: https://doi.org/10.1103/9891-x33t

Abstract

Ground-state energy and matrix elements are reconstructed from correlators in lattice QCD by diagonalizing transfer matrix T^ within the Krylov subspace spanned by T^n|χ⟩, where |χ⟩ is a state generated by an interpolating field on the lattice. In numerical applications, this strategy is spoiled by statistical noise. To circumvent the problem, we introduce a low-rank approximation based on a singular-value decomposition of a matrix made of the correlators. The associated bias is eliminated by an extrapolation to the limit of vanishing variance of energy eigenvalues. The strategy is tested using a set of mock data as well as real data of K and Ds meson correlators.

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Phys. Rev. D 113, 054514– Published 31 March, 2026
  • Received 14 November 2025
  • Accepted 5 March 2026
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