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Title: Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields

Abstract

There has been much recent progress in the understanding and reduction of the computational cost of the hybrid Monte Carlo algorithm for lattice QCD as the quark mass parameter is reduced. In this letter we present a new solution to this problem, where we represent the fermionic determinant using n pseudofermion fields, each with an nth root kernel. We implement this within the framework of the rational hybrid Monte Carlo algorithm. We compare this algorithm with other recent methods in this area and find it is competitive with them.

Authors:
;  [1];  [2]
  1. Center for Computational Sciences, Boston University, 3 Cummington Street, Boston, Massachusetts 02215 (United States)
  2. (United Kingdom)
Publication Date:
OSTI Identifier:
20955413
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevLett.98.051601; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; MATHEMATICAL SOLUTIONS; MONTE CARLO METHOD; QUANTUM CHROMODYNAMICS; QUARKS

Citation Formats

Clark, M. A., Kennedy, A. D., and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ. Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.051601.
Clark, M. A., Kennedy, A. D., & School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ. Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields. United States. doi:10.1103/PHYSREVLETT.98.051601.
Clark, M. A., Kennedy, A. D., and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ. Fri . "Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields". United States. doi:10.1103/PHYSREVLETT.98.051601.
@article{osti_20955413,
title = {Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields},
author = {Clark, M. A. and Kennedy, A. D. and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ},
abstractNote = {There has been much recent progress in the understanding and reduction of the computational cost of the hybrid Monte Carlo algorithm for lattice QCD as the quark mass parameter is reduced. In this letter we present a new solution to this problem, where we represent the fermionic determinant using n pseudofermion fields, each with an nth root kernel. We implement this within the framework of the rational hybrid Monte Carlo algorithm. We compare this algorithm with other recent methods in this area and find it is competitive with them.},
doi = {10.1103/PHYSREVLETT.98.051601},
journal = {Physical Review Letters},
number = 5,
volume = 98,
place = {United States},
year = {Fri Feb 02 00:00:00 EST 2007},
month = {Fri Feb 02 00:00:00 EST 2007}
}
  • Improved staggered-fermion formulations are a popular choice for lattice QCD calculations. Historically, the algorithm used for such calculations has been the inexact R algorithm, which has systematic errors that only vanish as the square of the integration step size. We describe how the exact rational hybrid Monte Carlo (RHMC) algorithm may be used in this context, and show that for parameters corresponding to current state-of-the-art computations it leads to a factor of approximately seven decrease in cost as well as having no step-size errors.
  • The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment (dt) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator's spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggeredmore » quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions (chiQCD). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds.« less
  • The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment (dt) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator's spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggeredmore » quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions ({chi}QCD). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds.« less
  • Hybrid Monte Carlo simulations that implement the fermion action using multiple terms are commonly used. By the nature of their formulation they involve multiple integration time scales in the evolution of the system through simulation time. These different scales are usually dealt with by the Sexton-Weingarten nested leapfrog integrator. In this scheme the choice of time scales is somewhat restricted as each time step must be an exact multiple of the next smallest scale in the sequence. A novel generalisation of the nested leapfrog integrator is introduced which allows for far greater flexibility in the choice of time scales, asmore » each scale now must only be an exact multiple of the smallest step size.« less
  • We present first results obtained from a simulation of lattice QCD with staggered fermions by a Monte Carlo algorithm that incorporates the effect of the fermion determinant exactly. The chiral condensate chi-barchi and various Wilson-loop expectation values are measured on a 4/sup 4/ space-time lattice and the results are compared with the same quantities measured on the same-size lattice with the pseudofermion method. A quantitatively good agreement is found.