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

Abstract

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.

Journal version. Added ancillary correlation function data and Mathematica notebook to reproduce analysis and plots

Cited by in corpus (1)

• On the equivalence of Prony and Lanczos methods for Euclidean correlation functions