Description
A Practical Approach to Preserving Chirality in Lattice QCD: Kenney-Laub Rational Approximation to the Overlap Operator Abstract: We present a practical approach for implementing the overlap Dirac operator in lattice QCD that combines the Kenney–Laub (KL) rational iterates for the matrix sign function, their partial fraction decomposition enabling Multi-Shift Conjugate Gradient solvers, and the parameter-free Brillouin operator as kernel. This method requires no spectral information, avoiding the costly eigenvalue estimates common in other methods, while systematically improving chiral symmetry preservation with approximation order. Preliminary benchmarking against the widely-used Chebyshev approach indicates that the KL method exhibits more predictable, monotonic convergence with improved efficiency. Physical observables, including PCAC mass and critical bare mass, show the KL-Brillouin combination to be especially effective: the Brillouin kernel outperforms the Wilson kernel, and equivalent precision can be reached with roughly 20% fewer computational resources. With minimal parameter tuning, no spectral input, and systematically improvable convergence, the method offers a straightforward and efficient alternative for overlap operator implementations where chiral symmetry is essential.