Unbiased Krylov subspace method for the extraction of ground state from lattice correlators
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914568315338752 |
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| author | Tsuji, Ryutaro Hashimoto, Shoji Kellermann, Ryan |
| author_facet | Tsuji, Ryutaro Hashimoto, Shoji Kellermann, Ryan |
| contents | 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 $\hat{T}^n|χ\rangle$, where $|χ\rangle$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_05058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unbiased Krylov subspace method for the extraction of ground state from lattice correlators Tsuji, Ryutaro Hashimoto, Shoji Kellermann, Ryan High Energy Physics - Lattice 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 $\hat{T}^n|χ\rangle$, where $|χ\rangle$ 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. |
| title | Unbiased Krylov subspace method for the extraction of ground state from lattice correlators |
| topic | High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2511.05058 |