Speeding up finite step-size updating of full QCD on the lattice

Abstract

We propose various improvements of finite step-size updating for full QCD on the lattice that might turn finite step-size updating into a viable alternative to the hybrid Monte Carlo algorithm. These improvements are noise reduction of the noisy estimator of the fermion determinant, unbiased inclusion of the hopping parameter expansion and a multi-level Metropolis scheme. First numerical tests are performed for the 2 dimensional Schwinger model with two flavours of Wilson fermions and for QCD with two flavours of Wilson fermions and Schrödinger functional boundary conditions. *

Lattice QCD and the Schwarz alternating procedure

“…acceptance-rejection step to correct for the quark determinant [7]- [11]. Following the lines of subsection 5.2, the random pseudo-fermion field that needs to be introduced in the correction step can be reduced to the support of Q Λ − Q Λ in this case.…”

“…The design of simulation algorithms for lattice QCD that operate on overlapping blocks of lattice points is non-trivial, however, because the global correctness of the simulation must be guaranteed. In principle the problem can be solved using stochastic acceptancerejection steps similar to those previously considered by Hasenbusch [7] (see also refs. [8]- [11]).…”

Fermions as global correction in lattice QCD

“…Via (2.4) the exact acceptance rate can also be determined from the variance. 2 The exact acceptance rates as determined from the variances are plotted in fig. 2 together with the result of a linear fit to σ 2 2 (V ) constrained to zero.…”

“…The proposed changes of the gauge configuration come from a hierarchical filter (section 2) that separates short and long distance physics. Hierarchical filters based on approximations of the determinant with increasing accuracy were introduced and tested in [2]. The advantage of our approach, based on recursive domain decomposition, is that it allows for a decoupling of updates within the domains and thus parallel domain-wise acceptance steps in the filter (section 3).…”

Lattice QCD with light dynamical quarks

“…Inspired by [11] (see also [12]) we tried to improve autocorrelations by "determinant breakup". In our case this means, for instance, that simulating two flavours separately should be more effective than two degenerate flavours together.…”