The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them, normalized to the one with vacuum quantum numbers, by a Monte Carlo procedure whose cost increases power-like with the time extent of the lattice. This is achieved thanks to a multi-level integration scheme, inspired by the transfer matrix formalism, which exploits the symmetry and the locality in time of the underlying statistical system. As a result the cost of computing the lowest energy level in a given channel, its multiplicity and its matrix elements is exponentially reduced with respect to the standard path-integral Monte Carlo. We briefly illustrate the approach in the simple case of the one-dimensional harmonic oscillator and discuss in some detail its extension to the four-dimensional Yang Mills theories. We report on our recent new results in the SU(3) Yang--Mills theory on the relative contribution to the partition function of the parity-odd states

Della Morte, M., Giusti, L. (2009). Symmetries and exponential error reduction in YM theories on the lattice: Theoretical aspects and simulation results. In Lattice2009. Sissa Medialab Srl.

Symmetries and exponential error reduction in YM theories on the lattice: Theoretical aspects and simulation results

Giusti, L
2009

Abstract

The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them, normalized to the one with vacuum quantum numbers, by a Monte Carlo procedure whose cost increases power-like with the time extent of the lattice. This is achieved thanks to a multi-level integration scheme, inspired by the transfer matrix formalism, which exploits the symmetry and the locality in time of the underlying statistical system. As a result the cost of computing the lowest energy level in a given channel, its multiplicity and its matrix elements is exponentially reduced with respect to the standard path-integral Monte Carlo. We briefly illustrate the approach in the simple case of the one-dimensional harmonic oscillator and discuss in some detail its extension to the four-dimensional Yang Mills theories. We report on our recent new results in the SU(3) Yang--Mills theory on the relative contribution to the partition function of the parity-odd states
slide + paper
Lattice gauge theory, Yang--Mills, glueballs, algorithms
English
27th International Symposium on Lattice Field Theory, LAT 2009
2009
Lattice2009
2009
91
029
http://pos.sissa.it//archive/conferences/091/029/LAT2009_029.pdf
none
Della Morte, M., Giusti, L. (2009). Symmetries and exponential error reduction in YM theories on the lattice: Theoretical aspects and simulation results. In Lattice2009. Sissa Medialab Srl.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/24997
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