1997/07/08 by Christopher Thron, C. Thron, S. J. Dong +2 · 93 citations
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Diagonal #Estimator #Geometry #Markov Chains and Monte Carlo Methods #Mathematics #Monte Carlo method #Quantum Chromodynamics and Particle Interactions #Statistics #Theoretical and Computational Physics #hep-lat
paper · pdf · doi:10.1103/physrevd.57.1642
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 57(3), 1642-1653 (American Physical Society) · 24 pages, 10 figures, LaTeX, epsf.sty
arxiv created 1997/07/08 · openalex publication_date 1998/02/01 · openalex created_date 2016/06/24 · arxiv updated 2016/08/24 · openalex updated_date 2026/08/05
We introduce the Pad'e-Z2 (PZ) stochastic estimator for calculating determinants and determinant ratios. The estimator is applied to the calculation of fermion determinants from the two ends of the hybrid Monte Carlo trajectories with pseudofermions. Our results on the 83\ifmmode×\else\texttimes\fi12 lattice with Wilson action show that the statistical errors from the stochastic estimator can be reduced by more than an order of magnitude by employing an unbiased variational subtraction scheme which utilizes the off-diagonal matrices from the hopping expansion. Having been able to reduce the error of the determinant ratios to about 20% with a relatively small number of noise vectors, this may become a feasible algorithm for simulating dynamical fermions in full QCD. We also discuss the application to the density of states in Hamiltonian systems.