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arXiv · 2406.20009

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

Michael L. Wagman
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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.

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Michael L. Wagman. 2024-06-28. Lanczos, the transfer matrix, and the signal-to-noise problem. https://arxiv.org/abs/2406.20009

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