Symmetries and exponential error reduction in Yang-Mills theories on the lattice
arXiv:0806.2601 · doi:10.1016/j.cpc.2009.03.009
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.
arXiv comment18 pages, 4 figures. Few typos corrected, data sets added, Appendix A added. To appear on Comput. Phys. Commun
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