MINIMIZING STORAGE IN IMPLEMENTATIONS OF THE OVERLAP LATTICE-DIRAC OPERATOR

1998/11/16 by Herbert Neuberger · 32 citations
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Algorithm #Computer science #Dirac operator #Discrete mathematics #Implementation #Lattice (music) #Mathematical analysis #Mathematics #Operator (biology) #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Sign (mathematics) #Spectral Theory in Mathematical Physics #hep-lat

paper · pdf · doi:10.1142/s012918319900084x

published in International Journal of Modern Physics C 10(06), 1051-1057 (World Scientific) · 7 pages, plain TeX; minor errors corrected

arxiv created 1998/11/16 · openalex publication_date 1999/09/01 · arxiv updated 2015/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The overlap lattice-Dirac operator contains the sign function ∊(H). Recent practical implementations replace ∊(H) by a ratio of polynomials, H P n (H 2 )/Q n (H 2 ), and require storage of 2n+2 large vectors. Here I show that one can use only four large vectors at the cost of executing the core conjugate algorithm twice. The slow-down might be less than by a factor of 2, depending on the architecture of the computer one uses.

Citations

• Infinitely many regulator fields for chiral fermions
• A simulation of the Schwinger model in the overlap formalism

Cited by

• Study ofΘ+(ududs¯)in lattice QCD with exact chiral symmetry
• Efficient implementation of the overlap operator on multi-GPUs
• One-loop renormalization of fermionic currents with the overlap-Dirac operator
• Light quark masses, chiral condensate and quark–gluon condensate in quenched lattice QCD with exact chiral symmetry