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Multigrid Preconditioning for the Overlap Operator in Lattice QCD
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The overlap operator is a lattice discretization of the Dirac operator of quantum chromodynamics, the fundamental physical theory of the strong interaction between the quarks. As opposed to other discretizations it preserves the important physical property of chiral symmetry, at the expense of requiring much more effort when solving systems with this operator. We present a preconditioning technique based on another lattice discretization, the Wilson-Dirac operator. The mathematical analysis precisely describes the effect of this preconditioning in the case that the Wilson-Dirac operator is normal. Although this is not exactly the case in realistic settings, we show that current smearing techniques indeed drive the Wilson-Dirac operator towards normality, thus providing a motivation why our preconditioner works well in computational practice. Results of numerical experiments in physically relevant settings show that our preconditioning yields accelerations of up to one order of magnitude.
Forward citations
Cited by 4 Pith papers
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Diagonal Kenney-Laub Rational Approximation to the Overlap Operator using Wilson and Brillouin Kernel
Diagonal Kenney-Laub rational approximation to the overlap operator using Wilson and Brillouin kernels shows enhanced chiral symmetry preservation and efficiency over Chebyshev polynomials on quenched lattices.
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QCD Anderson transition with overlap valence quarks on a twisted-mass sea -- an update
New lattice data show the quark mobility edge in QCD stays near 86-88 MeV at temperatures close to the chiral transition, instead of vanishing as previously extrapolated.
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Chiral rank-$k$ truncations for the multigrid preconditioner of Wilson fermions in lattice QCD
An SVD-based rank-k truncation of chirally split test vectors reduces Wilson fermion multigrid solve times on HSC and MILC ensembles.
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Performance of Low Mode Averaging on Twisted-Mass Fermion Ensembles at the physical pion mass point
Numerical tests show low-mode averaging reduces noise in light meson and baryon observables on physical-pion twisted-mass ensembles, yielding renormalized chiral condensate 269.5(4.5) MeV.
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