Block Lanczos algorithm for lattice QCD spectroscopy and matrix elements

Hackett, Daniel C.; Wagman, Michael L.

doi:10.1103/fp74-q35q

Block Lanczos algorithm for lattice QCD spectroscopy and matrix elements

Journal Article · Fri Jul 25 04:00:00 EDT 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/fp74-q35q· OSTI ID:2482471

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

Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious eigenvalue filtering with the Cullum-Willoughby test. Here, we extend this framework to the analysis of correlation-function matrices built from multiple interpolating operators in lattice quantum chromodynamics (QCD) by constructing an oblique generalization of the block Lanczos algorithm, as well as a new physically motivated reformulation of the Cullum-Willoughby test that generalizes to block Lanczos straightforwardly. The resulting block Lanczos method directly extends generalized eigenvalue problem (GEVP) methods, which can be viewed as applying a single iteration of block Lanczos. Block Lanczos provides qualitative and quantitative advantages over GEVP methods analogous to the benefits of Lanczos over the standard effective mass, including faster convergence to ground- and excited-state energies, explicitly computable two-sided error bounds, straightforward extraction of matrix elements of external currents, and asymptotically constant signal-to-noise. No fits or statistical inference are required. Proof-of-principle calculations are performed for noiseless mock-data examples as well as two-by-two proton correlation-function matrices in lattice QCD.

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); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF); National Energy Research Scientific Computing Center (NERSC)

Grant/Contract Number:: 89243024CSC000002; AC02-05CH11231; AC05-00OR22725

OSTI ID:: 2482471

Report Number(s):: FERMILAB-PUB--24-0875-T; arXiv:2412.04444; oai:inspirehep.net:2856227

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 1 Vol. 112; ISSN 2470-0010; ISSN 2470-0029

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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