Spin on the lattice

I review the current status of hadronic structure computations on the lattice. I describe the basic lattice techniques and difficulties and present some of the latest lattice results; in particular recent results of the RBC group using domain wall fermions are also discussed.Comment: 10 pages, 10 figures, plenary talk given at SPIN2002, BNL, updated references, corrected typo

Nuclear Physics from Lattice QCD

This is the final report for this project

Computing and deflating eigenvalues while solving multiple right hand side linear systems in Quantum Chromodynamics

We present a new algorithm that computes eigenvalues and eigenvectors of a Hermitian positive definite matrix while solving a linear system of equations with Conjugate Gradient (CG). Traditionally, all the CG iteration vectors could be saved and recombined through the eigenvectors of the tridiagonal projection matrix, which is equivalent theoretically to unrestarted Lanczos. Our algorithm capitalizes on the iteration vectors produced by CG to update only a small window of vectors that approximate the eigenvectors. While this window is restarted in a locally optimal way, the CG algorithm for the linear system is unaffected. Yet, in all our experiments, this small window converges to the required eigenvectors at a rate identical to unrestarted Lanczos. After the solution of the linear system, eigenvectors that have not accurately converged can be improved in an incremental fashion by solving additional linear systems. In this case, eigenvectors identified in earlier systems can be used to deflate, and thus accelerate, the convergence of subsequent systems. We have used this algorithm with excellent results in lattice QCD applications, where hundreds of right hand sides may be needed. Specifically, about 70 eigenvectors are obtained to full accuracy after solving 24 right hand sides. Deflating these from the large number of subsequent right hand sides removes the dreaded critical slowdown, where the conditioning of the matrix increases as the quark mass reaches a critical value. Our experiments show almost a constant number of iterations for our method, regardless of quark mass, and speedups of 8 over original CG for light quark masses.Comment: 22 pages, 26 eps figure

First Calculation of Hyperon Axial Couplings from Lattice QCD

In this work, we report the first lattice calculation of hyperon axial couplings, using the 2+1-flavor MILC configurations and domain-wall fermion valence quarks. Both the $\Sigma$ and $\Xi$ axial couplings are computed for the first time in lattice QCD. In particular we find that $g_{\Sigma\Sigma} = 0.450(21)_{\rm stat}(27)_{\rm syst}$ and $g_{\Xi\Xi} = -0.277(15)_{\rm stat}(19)_{\rm syst}$.Comment: 5 pages, 2 figure

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).Comment: 27 pp. main text, 4 pp. appendices, 30 pp. reference

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021)