Local multiboson factorization of the quark determinant
Many correlators in lattice QCD show an exponential degradation of the signal-to-noise ratio with distance. This problem can be addressed by performing multilevel Monte Carlo sampling. However, to date, multilevel techniques have been limited to bosonic theories.
To overcome this limitation, we developed a factorization into independent spacetime domains of the Wilson fermions determinant contribution to the path integral of lattice QCD. We studied in detail the numerical properties of the operator mediating inter-domain interactions, and proposed to represent its determinant by a path integral over multiboson fields, living on the domain boundaries. On the contrary, the intra-domain contribution to the determinant is represented by ordinary pseudofermion fields with suitable boundary conditions. We implemented the factorization in a HMC algorithm that allows to update the gauge field independently in different domains.
Thanks to this factorization, combined with a matching domain decomposition of observables, it is possible to perform multilevel Monte Carlo sampling in QCD for the first time with dynamical fermions.
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