Abstract
The Wilson fermion determinant can be written as product of the determinants of two hermitian positive definite matrices. This formulation allows to simulate non-degenerate quark flavors by means of the hybrid Monte Carlo algorithm. A major numerical difficulty is the occurrence of nested inversions. We construct a Uzawa iteration scheme which treats the nested system within one iterative process.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Caso et al. (Particle Data Group). Review of particle properties. European Phys. Tour., C3, 77–169 1999.
J. Gasser and H. Leutwyler. Quark masses. Phys. Rept., 87:77–169, 1982.
A. Frommer, V. Hannemann, B. Nöckel, Th. Lippert, and K. Schilling. Accelerating Wilson fermion matrix inversions by means of the stabilized biconjugate gradient algorithm. Int. J. Mod. Phys., C5:1073, 1994.
S. Fischer, A. Frommer, U. Glässner, Th. Lippert, G. Ritzenhöfer, and K. Schilling. A parallel SSOR preconditioner for lattice QCD. Comp. Phys. Commun., 98:20–34, 1996.
S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth. Hybrid Monte Carlo. Phys. Lett.,B195:216, 1987.
S. Gottlieb, W. Liu, D. Toussaint, R. L. Renken, and R. L. Sugar. Hybrid molecular dynamics algorithms for the numerical simulation of quantum chromodynamics. Phys. Rev.,D35:2531, 1987.
D. H. Weingarten and D. N. Petcher. Monte Carlo integration for lattice gauge theories with fermions. Phys. Lett.,B99:333, 1981.
K. G. Wilson. Quarks: from paradox to myth. In New Phenomena In Subnuclear Physics,volume Part A, pages 13–22. New York, 1977, 1975. Proceedings of Erice summer school, Erice.
H. Neuberger. The overlap Dirac operator. In Frommer et al. [21]. These proceedings.
S. Sharpe and N. Shoresh. Partially quenched QCD with non-degenerate dynamical quarks. 1999.
N. Eicker, P. Lacock, K. Schilling, A. Spitz, U. Glässner, S. Güsken, H. Hoeber, Th. Lippert, Th. Struckmann, P. Ueberholz, and J. Viehoff. Light and strange hadron spectroscopy with dynamical Wilson fermions. Phys. Rev., D59:014509, 1999.
A. Ali Khan et al. Light hadron spectrum and quark masses in QCD with two flavors of dynamical quarks. hep-lat/9909050, 1999.
Claude Bernard et al. The static quark potential in three flavor qcd. 2000.
A. Peikert, F. Karsch, E. Laermann, and B. Sturm. The three flavour chiral phase transition with an improved quark and gluon action in lattice QCD. Nucl. Phys. Proc. Suppl., 73:468, 1999.
M. Löscher. A new approach to the problem of dynamical quarks in numerical simulations of lattice QCD. Nucl. Phys., B418:637–648, 1994.
C. Alexandrou et al. The deconfinement phase transition in one-flavor QCD. Phys. Rev., D60:034504, 1999.
C. Alexandrou et al. Thermodynamics of one-flavour QCD. Preprint heplat/9806004, 1998.
I. Montvay. Least-squares optimized polynomials for fermion simulations. In Frommer et al. [21]. These proceedings. 1998
Th. Lippert. The hybrid Monte Carlo algorithm for quantum chromodynamics. In H. Meyer-Ortmanns and A. Klümper, editors, Field theoretical tools for polymer and particle physics, volume 508 of Lecture Notes in Physics, pages 122–131. Springer Verlag, Heidelberg, 1998. Proceedings of Workshop of the Graduiertenkolleg at the University of Wuppertal, June, 1997.
J. H. Bramble, J. E. Pasciak, and A. T. Vassilev. Analysis of the inexact Uzawa algorithm for saddle point problems. SIAM J. Numer. Anal., 34:1072–1092, 1997.
A. Frommer, Th. Lippert, B. Medeke, and K. Schilling, editors. Numerical Challenges in Lattice QCD. Springer Verlag, Heidelberg, 2000. Proceedings of International Workshop, University of Wuppertal, August 22–24, 1999, Present proceedings.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lippert, T. (2000). One-Flavour Hybrid Monte Carlo with Wilson Fermions. In: Frommer, A., Lippert, T., Medeke, B., Schilling, K. (eds) Numerical Challenges in Lattice Quantum Chromodynamics. Lecture Notes in Computational Science and Engineering, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58333-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-58333-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67732-1
Online ISBN: 978-3-642-58333-9
eBook Packages: Springer Book Archive