Review on Algorithms for dynamical fermions

Abstract

This review discusses the current and next steps in research of algorithms for dynamical fermions in large scale lattice QCD simulations. First a short overview on the state-of-the-art of ensemble generation at the physical point is given. Followed by an overview on required steps towards simulation of large lattices for the Hybrid Monte Carlo algorithm. Here, in particular, the status of iterative solvers and tuning procedures for numerical integrators within the molecular dynamics are discussed. This is followed by a review on the on-going developments for algorithms, with a focus on methods which are potentially useful to simulate gauge theories at very fine lattice spacings, i.e. well suited to overcome freezing of the topological charge. This includes modification of the HMC algorithm as well as a discussion of algorithms which includes the fermion weight via global correction steps. Parts of the discussions are on the application of generative models via gauge equivariant flows as well as multi-level algorithms.

Fine grinding localized updates via gauge equivariant flows in the 2D Schwinger model

“…Note that all filter steps before the global correction steps are local and can be perform in parallel, making the approach scalable and inline with current algorithmic trends such as highlighted in [2,21]. Moreover, the approach can be easily generalized to the multi-level procedure [22,23], which would not only help to fight against long autocorrelation times but also mitigate exponential increasing noise in the long-distance measurements of correlators.…”

“…Especially in gauge theories, this is even more severe due to topological freezing. Due to that it is currently not feasible to simulate with state-of-the-art algorithms at very fine lattice spacings below 𝑎 < 0.04 fm with periodic boundary conditions, see for a review [2]. However, if possible, simulations at very fine lattice spacings have a major impact on measurements in lattice QCD, namely by stabilising continuum extrapolations which would enable a robust way to make advances at the precision frontier of the standard model of particle physics.…”

Use of Schwinger-Dyson equation in constructing an approximate trivializing map

“…There have been many attempts to overcome the critical slowing down [2][3][4][5][6][7][8][9][10][11][12][13], and recent studies are presented thoroughly at the conference [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. We in this work concentrate on developing the idea of the trivializing map proposed by Lüscher [7] (cf.…”