Speaker
Description
We present a practical approach for implementing the overlap Dirac operator in Lattice QCD, combining the diagonal Kenney-Laub (KL) rational iterates for approximating the matrix sign function with the Brillouin operator as overlap kernel. The partial fraction decomposition of the KL iterates enables multi-shift conjugate gradient solvers, with all weights and shifts given by closed-form trigonometric expressions that depend only on the approximation order. No extreme eigenvalue estimates are required, neither for determining the decomposition constants nor for rescaling the overlap operator kernel.
Preliminary benchmarking against the Zolotarev optimal rational and Chebyshev polynomial approximations shows that the KL method delivers competitive efficiency with a qualitative advantage: convergence with approximation order is smooth and monotonic on all diagnostic quantities tested, including the Ginsparg-Wilson violation, PCAC mass, and critical bare mass, with indications of reduced statistical noise. The KL-Brillouin combination consistently reaches a target precision at lower computational cost than the Wilson-kernel counterpart, with the Brillouin kernel's improved spectral conditioning compensating for its higher per-application cost. With minimal parameter tuning, no spectral input, and predictable convergence behavior, the method offers a straightforward alternative for calculations in which exact or near-exact chiral symmetry is essential.