Algorithms for lattice QCD and related models

• Applicant: Dr. Martin Herbert Hasenbusch
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2016 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 321114788

Lattice QCD is the standard method for the theoretical study of strong interactions beyond perturbation theory. Quantitative results for hadronic properties are usually obtained from Monte Carlo simulations. The numerical task is however challenging. In particular the proper treatment of sea quarks is demanding. Nethertheless, in the four decades of its existance it matured and today allows us to compute many observables of interest to QCD phenomenology to good accuracy. Technical progress in lattice QCD has been driven from the increase of computational power and advances in algorithms. In this proposal we focus on the latter.In the last two decades, there has been much progress in the treatment of dynamical sea quarks. Large scale simulations rely on the representation of the fermion determinant by an integral over auxiliary fields. In its simplest form, this idea goes back to Petcher and Weingarten in 1981. The standard algorithm is the Hybrid Monte Carlo (HMC) algorithm proposed by Duane et al. in 1987. For the implementation used until about 2000, the numerical effort increased strongly with decreasing fermion mass. As a result, the masses that could be reached were far too large compared with those of the up and down quarks. Since then, the situation has been much improved by solvers that show a better behavior with decreasing fermion mass and by less noisy integral representations of the fermion determinant. The simplest of these is the mass preconditioning introduced in 1999 by myself. Similar in spirit is the domain decomposition (DD) HMC algorithm proposed by Lüscher. Here we shall exploit the idea of domain decomposition in temporal direction only. In particular we shall put domain decomposition on top of even/odd preconditioning. Further motivation for the domain decomposition in temporal only comes from the proposal of Ce, Giusti and Schaefer for a variance reduced estimator for fermionic correlation functions. With such estimators one is, for example, aiming at more accurate and reliable estimates of baryon masses. In lattice QCD one finds severe slowing down due to barriers between sectors of different topological charge. Lüscher proposed to overcome this problem by replacing periodic by open boundary conditions in temporal direction. Here we shall investigate parallel tempering, using different tempering parameters.Most Monte Carlo algorithms that are used to simulate spin models and lattice field theories today fulfill detailed balance. This enshures stabilty of the Markov chain. Recently it has been demonstrated for simple spin models that abandoning detailed balance, while keeping stability of course, considerable performance gains can be achieved. In the proposed project we like to push these ideas in the direction of lattice QCD. As a first step we shall implement the so called event driven Monte Carlo for princible chiral models. Within our project, we are aiming at the pure SU(3) gauge model.

• DFG Programme: Research Grants