2012/04/30 by Jacob Finkenrath, Francesco Knechtli, Björn Leder
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Dirac operator #Factorization #Fermion #Filter (signal processing) #Lattice (music) #Markov Chains and Monte Carlo Methods #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #hep-lat
paper · pdf · doi:10.1016/j.cpc.2013.01.020
36 pages, 9 figures; improved version to be published in Comput.Phys.Commun., new results for the topological charge presented in Figure 7
arxiv created 2013/01/29 · openalex publication_date 2013/02/04 · arxiv updated 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is widely believed that the fermion determinant cannot be treated in global acceptance-rejection steps of gauge link configurations that differ in a large fraction of the links. However, for exact factorizations of the determinant that separate the ultraviolet from the infrared modes of the Dirac operator it is known that the latter show less variation under changes of the gauge field compared to the former. Using a factorization based on recursive domain decomposition allows for a hierarchical algorithm that starts with pure gauge updates of the links within the domains and ends after a number of filters with a global acceptance-rejection step. Ratios of determinants have to be treated stochastically and we construct techniques to reduce the noise. We find that the global acceptance rate is high on moderate lattice sizes and demonstrate the effectiveness of the hierarchical filter.