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

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

2008-06-16

arxiv.org/abs/0806.2601v2

Comput.Phys.Commun.180:819-826,2009

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1016/j.cpc.2009.03.009

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.

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