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

Michele Della Morte, Leonardo Giusti

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

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.
OriginalsprogUdefineret/Ukendt
TidsskriftPoS LAT
StatusUdgivet - 13. okt. 2009

Bibliografisk note

13 pages, 7 figures, 1 table, presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, China

Emneord

  • hep-lat

Citer dette

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Symmetries and exponential error reduction in YM theories on the lattice : theoretical aspects and simulation results. / Morte, Michele Della; Giusti, Leonardo.

I: PoS LAT, 13.10.2009.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

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

T2 - theoretical aspects and simulation results

AU - Morte, Michele Della

AU - Giusti, Leonardo

N1 - 13 pages, 7 figures, 1 table, presented at the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, China

PY - 2009/10/13

Y1 - 2009/10/13

N2 - 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.

AB - 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.

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