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

TL;DR

This paper introduces an unbiased Krylov subspace method with a low-rank approximation and extrapolation to accurately extract ground-state energies from noisy lattice QCD correlators.

Contribution

A novel low-rank approximation and bias elimination technique for Krylov subspace methods applied to lattice QCD data.

Findings

Successfully tested on mock data and real meson correlators.

Eliminates bias caused by statistical noise in energy extraction.

Improves accuracy of ground-state energy reconstruction.

Abstract

Ground-state energy and matrix element are reconstructed from correlators in lattice QCD by diagonalizing transfer matrix $\hat{T}$ within the Krylov subspace spanned by $\hat{T}^n|\chi\rangle$, where $|\chi\rangle$ 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 eigenvalue. The strategy is tested using a set of mock data as well as real data of $K$ and $D_s$ meson correlators.