Local coherence and deflation of the low quark modes in lattice QCD

Abstract

The spontaneous breaking of chiral symmetry in QCD is known to be linked to a non-zero density of eigenvalues of the massless Dirac operator near the origin. Numerical studies of two-flavour QCD now suggest that the low quark modes are locally coherent to a certain extent. As a consequence, the modes can be simultaneously deflated, using local projectors, with a total computational effort proportional to the lattice volume (rather than its square). Deflation has potentially many uses in lattice QCD. The technique is here worked out for the case of quark propagator calculations, where large speed-up factors and a flat scaling behaviour with respect to the quark mass are achieved.

Plain TeX, 23 pages, 4 figures included; minor text modifications; version published in JHEP

References in corpus (1)

• Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry

Cited by in corpus (25)

• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• $D_s$ mesons with $DK$ and $D^{\ast }K$ scattering near threshold
• Light Hadron Masses from Lattice QCD
• Adaptive multigrid algorithm for the lattice Wilson-Dirac operator
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$ from lattice QCD: a complete calculation
• Adaptive Multigrid Algorithm for Lattice QCD
• Deflation acceleration of lattice QCD simulations
• A lattice investigation of exotic tetraquark channels
• Overlap Valence on 2+1 Flavor Domain Wall Fermion Configurations with Deflation and Low-mode Substitution
• Adaptive Aggregation-based Domain Decomposition Multigrid for Twisted Mass Fermions
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Symmetries of hadrons after unbreaking the chiral symmetry
• On the strength of the $U_A(1)$ anomaly at the chiral phase transition in $N_f=2$ QCD
• A local factorization of the fermion determinant in lattice QCD
• Lattice QCD with Domain Decomposition on Intel Xeon Phi Co-Processors
• Nucleon isovector couplings in Nf = 2 + 1 lattice QCD at the physical point
• Mellin moments of spin dependent and independent PDFs of the pion and rho meson
• Kenneth Wilson and lattice QCD
• Lattice results for the longitudinal spin structure and color forces on quarks in a nucleon
• Spectrum of QCD with one flavor: A window for supersymmetric dynamics
• Scale setting for $N_f=3+1$ QCD
• A fully non-perturbative charm-quark tuning using machine learning
• Neural-network preconditioners for solving the Dirac equation in lattice gauge theory
• A multigrid accelerated eigensolver for the Hermitian Wilson-Dirac operator in lattice QCD
• Chiral symmetry and taste symmetry from the eigenvalue spectrum of staggered Dirac operators