Related papers: Multi-level integration for meson propagators
We explore the possibility of computing fermionic correlators on the lattice by combining a domain decomposition with a multi-level integration scheme. The quark propagator is expanded in series of terms with a well defined hierarchical…
We introduce a factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a bosonic action which is local in the block fields. The interaction among gauge fields on distant blocks is mediated by…
We discuss the recently proposed multiboson domain-decomposed factorization of the gauge-field dependence of the fermion determinant in lattice QCD. In particular, we focus on the case of a lattice divided in an arbitrary number of thick…
The numerical computation of many hadronic correlation functions is exceedingly difficult due to the exponentially decreasing signal-to-noise ratio with the distance between source and sink. Multilevel integration methods, using independent…
The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are…
We introduce a multigrid multilevel Monte Carlo method for stochastic trace estimation in lattice QCD based on orthogonal projections. This formulation extends the previously proposed oblique decomposition and it is assessed on three…
In the last few years it has been proposed a one-dimensional factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a block-local action of the auxiliary bosonic fields. Here we propose a…
We investigate the combination of a two-level sampling algorithm with distillation techniques to compute disconnected fermionic correlation functions. The method relies on a factorization of the quark propagator into domain-local…
In lattice QCD the calculation of disconnected quark loops from the trace of the inverse quark matrix has large noise variance. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials on a…
Nested integration problems arise in various scientific and engineering applications, including Bayesian experimental design, financial risk assessment, and uncertainty quantification. These nested integrals take the form $\int f\left(\int…
We discuss and compare the efficiency of various methods, combinations of point-to-all propagators, stochastic timeslice-to-all propagators, the one-end trick and sequential propagators, to compute two-point correlation functions of…
The strong coupling limit of lattice QCD with staggered fermions has been studied for decades, both via Monte Carlo and via mean field theory. In this model, the finite density sign problem can be made mild and the full phase diagram can be…
Perturbative expansions of several small Wilson loops are computed through next-to-next-to-leading order in unquenched lattice QCD, from Monte Carlo simulations at weak couplings. This approach provides a much simpler alternative to…
In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty…
The calculation of disconnected diagram contributions to physical signals is a computationally expensive task in Lattice QCD. To extract the physical signal, the trace of the inverse Lattice Dirac operator, a large sparse matrix, must be…
We develop an implementation for a recently proposed Noisy Monte Carlo approach to the simulation of lattice QCD with dynamical fermions by incorporating the full fermion determinant directly. Our algorithm uses a quenched gauge field…
The scalar two-loop master diagram is revisited in the massive cases needed for the computation of boson and fermion propagators in QED and QCD. By means of the causal method it is possible in a straightforward manner to express the…
Motivated by the application of L\"uscher's finite volume method to the study of the lightest scalar resonance in the $\pi\pi \to \pi\pi$ isoscalar channel, in this article we describe our studies of multi-pion correlation functions…
In these proceedings we address the computation of quark-line disconnected diagrams in lattice QCD. The evaluation of these diagrams is required for many phenomenologically interesting observables, but suffers from large statistical errors…
Computing disconnected diagrams in Lattice QCD (operator insertion in a quark loop) entails the computationally demanding problem of taking the trace of the all to all quark propagator. We first outline the basic algorithm used to compute a…