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.
Della Morte, M., Giusti, L. (2009). Symmetries and exponential error reduction in Yang-Mills theories on the lattice. COMPUTER PHYSICS COMMUNICATIONS, 180, 819-826 [10.1016/j.cpc.2009.03.009].
Symmetries and exponential error reduction in Yang-Mills theories on the lattice
GIUSTI, LEONARDO
2009
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.