Numerical techniques for lattice QCD in the $\epsilon$--regime

TL;DR

This paper discusses numerical techniques to improve lattice QCD simulations in the epsilon-regime, enabling more accurate determination of chiral Lagrangian parameters by addressing low eigenvalues of the Dirac operator.

Contribution

It introduces specific numerical methods, such as low-mode preconditioning and adapted-precision algorithms, to enhance the safety and efficiency of lattice QCD computations in the epsilon-regime.

Findings

Techniques significantly improve computational efficiency.

Methods ensure numerical safety in low eigenvalue regimes.

Facilitates precise parameter extraction in lattice QCD.

Abstract

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the physical extent of the lattice is much smaller than the Compton wave length of the pion. The use of a formulation of the lattice theory that preserves chiral symmetry is attractive in this context, but the numerical implementation of any such approach requires special care in this kinematical situation due to the presence of some very low eigenvalues of the Dirac operator. We discuss a set of techniques (low-mode preconditioning and adapted-precision algorithms in particular) that make such computations numerically safe and more efficient by a large factor.