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

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 ${\hat{T}}^n|\chi ⟩$, where $|\chi ⟩$ 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.

33 pages, 25 figures