Symmetries and exponential error reduction in Yang-Mills theories on the lattice

Michele Della Morte, Leonardo Giusti

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the corresponding transfer matrix elements can be exploited to devise a multi-level Monte Carlo integration scheme for computing correlation functions whose numerical cost, at a fixed precision and at asymptotically large times, increases power-like with the time extent of the lattice. As a result the numerical effort is exponentially reduced with respect to the standard Monte Carlo procedure. We test this strategy in the SU(3) Yang--Mills theory by evaluating the relative contribution to the partition function of the parity odd states.
OriginalsprogUdefineret/Ukendt
TidsskriftComput.Phys.Commun.
DOI
StatusUdgivet - 16. jun. 2008

Bibliografisk note

18 pages, 4 figures. Few typos corrected, data sets added, Appendix A added. To appear on Comput. Phys. Commun

Emneord

  • hep-lat
  • cond-mat.mtrl-sci
  • cond-mat.stat-mech

Citer dette

@article{42b96d6b17df4e9b9274ae3ba2b6a06e,
title = "Symmetries and exponential error reduction in Yang-Mills theories on the lattice",
abstract = "The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the corresponding transfer matrix elements can be exploited to devise a multi-level Monte Carlo integration scheme for computing correlation functions whose numerical cost, at a fixed precision and at asymptotically large times, increases power-like with the time extent of the lattice. As a result the numerical effort is exponentially reduced with respect to the standard Monte Carlo procedure. We test this strategy in the SU(3) Yang--Mills theory by evaluating the relative contribution to the partition function of the parity odd states.",
keywords = "hep-lat, cond-mat.mtrl-sci, cond-mat.stat-mech",
author = "Morte, {Michele Della} and Leonardo Giusti",
note = "18 pages, 4 figures. Few typos corrected, data sets added, Appendix A added. To appear on Comput. Phys. Commun",
year = "2008",
month = "6",
day = "16",
doi = "10.1016/j.cpc.2009.03.009",
language = "Udefineret/Ukendt",
journal = "Computer Physics Communications",
issn = "0010-4655",
publisher = "Elsevier",

}

Symmetries and exponential error reduction in Yang-Mills theories on the lattice. / Morte, Michele Della; Giusti, Leonardo.

I: Comput.Phys.Commun., 16.06.2008.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Symmetries and exponential error reduction in Yang-Mills theories on the lattice

AU - Morte, Michele Della

AU - Giusti, Leonardo

N1 - 18 pages, 4 figures. Few typos corrected, data sets added, Appendix A added. To appear on Comput. Phys. Commun

PY - 2008/6/16

Y1 - 2008/6/16

N2 - The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the corresponding transfer matrix elements can be exploited to devise a multi-level Monte Carlo integration scheme for computing correlation functions whose numerical cost, at a fixed precision and at asymptotically large times, increases power-like with the time extent of the lattice. As a result the numerical effort is exponentially reduced with respect to the standard Monte Carlo procedure. We test this strategy in the SU(3) Yang--Mills theory by evaluating the relative contribution to the partition function of the parity odd states.

AB - The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the corresponding transfer matrix elements can be exploited to devise a multi-level Monte Carlo integration scheme for computing correlation functions whose numerical cost, at a fixed precision and at asymptotically large times, increases power-like with the time extent of the lattice. As a result the numerical effort is exponentially reduced with respect to the standard Monte Carlo procedure. We test this strategy in the SU(3) Yang--Mills theory by evaluating the relative contribution to the partition function of the parity odd states.

KW - hep-lat

KW - cond-mat.mtrl-sci

KW - cond-mat.stat-mech

U2 - 10.1016/j.cpc.2009.03.009

DO - 10.1016/j.cpc.2009.03.009

M3 - Tidsskriftartikel

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

ER -