Recent work [M. L. Wagman, Lanczos, the transfer matrix, and the signal-to-noise problem, .] found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multistate fit results than effective masses—but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of “spurious-state filtering” involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.
Hackett, Daniel C. and Wagman, Michael L.. "Lanczos algorithm for lattice QCD matrix elements." Physical Review D, vol. 112, no. 5, Sep. 2025. https://doi.org/10.1103/zjzt-rv86
Hackett, Daniel C., & Wagman, Michael L. (2025). Lanczos algorithm for lattice QCD matrix elements. Physical Review D, 112(5). https://doi.org/10.1103/zjzt-rv86
Hackett, Daniel C., and Wagman, Michael L., "Lanczos algorithm for lattice QCD matrix elements," Physical Review D 112, no. 5 (2025), https://doi.org/10.1103/zjzt-rv86
@article{osti_2440265,
author = {Hackett, Daniel C. and Wagman, Michael L.},
title = {Lanczos algorithm for lattice QCD matrix elements},
annote = {Recent work [M. L. Wagman, Lanczos, the transfer matrix, and the signal-to-noise problem, .] found that an analysis formalism based on the Lanczos algorithm allows energy levels to be extracted from Euclidean correlation functions with faster ground-state convergence than effective masses, convergent estimators for multiple states from a single correlator, and two-sided error bounds. After filtering out spurious eigenvalues and using outlier-robust estimators within a nested bootstrap framework, Lanczos estimators behave more like multistate fit results than effective masses—but without involving statistical fitting. We extend this formalism to the determination of matrix elements from three-point correlation functions and provide a physical picture of “spurious-state filtering” involving restriction to a Hermitian subspace. We demonstrate similar advantages for matrix elements as for spectroscopy through example applications to noiseless mock-data and (bare) forward matrix elements of the strange scalar current between both ground and excited states with the quantum numbers of the nucleon.},
doi = {10.1103/zjzt-rv86},
url = {https://www.osti.gov/biblio/2440265},
journal = {Physical Review D},
issn = {ISSN 2470-0029},
number = {5},
volume = {112},
place = {United States},
publisher = {American Physical Society (APS)},
year = {2025},
month = {09}}
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 9, Issue 1https://doi.org/10.1002/zamm.19290090105