Numerical techniques for lattice QCD in the $ε$--regime

Details Numerical techniques for lattice QCD in the $ε$--regime Numerical techniques for lattice QCD in the $ε$--regime

2002-12-06

arxiv.org/abs/hep-lat/0212012v1

Comput.Phys.Commun.153:31-51,2003

Physics

High Energy Physics

High Energy Physics - Lattice

Plain TeX source, 32 pages, figures included

Scientific paper

10.1016/S0010-4655(02)00874-3

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.

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