Algorithms for lattice QCD and related models
Final Report Abstract
The standard model of high energy physics describes the interactions of elementary particles: the electrodynamic, the weak and the strong interactions, while gravitation is not taken into account. Accurate results are obtained by using perturbation theory. This is in particular the case for Quantum electrodynamics (QED). For example, the magnetic moment of the electron could be computed up to 10 digits. Perturbation theory relies on the fact that the coupling constant is small. In the case of the strong interaction, described by quantum chromodynamics (QCD), the coupling constant increases with increasing distances or, equivalently, decreasing energies. As a result, low energy quantities, as for example the masses of hadrons are not accessible by perturbation theory. As a remedy, in 1974 K.G. Wilson proposed lattice QCD. It provides a mathematical definition of QCD beyond perturbation theory and hence opens the way to other computational tools. For example, the strong coupling expansion allowed to demonstrate the property of confinement. Today lattice QCD is mostly studied by Monte Carlo simulations. The method has matured to the point that it provides result that are of importance in particle phenomenology. Yet, despite the fact that a large fraction of the CPU time that is available on supercomputers is used for simulations of lattice QCD, more accurate results would be desirable. Therefore it is an obvious idea to work on the optimization of the algorithms that are used in these simulations. In my project, I have addressed primarily two problems: Incorporating fermions in the Monte Carlo simulation is notoriously difficult. For a long time it had been impossible to study fermions with masses as light as those of the lightest quarks, the up and down quarks. Only in the last decade this has been achieved due to algorithmic progress. Here I tried to combine different ideas in this direction. A moderate progress is achieved. In my opinion, further, more systematic studies along these lines are promising. The dynamics of topological objects in lattice QCD simulations slows down rapidly with decreasing lattice spacing. This makes it hard to go beyond a certain lattice resolution, which however would be desirable from a physics point of view. In the project I have investigated the so called tempering method to speed up the dynamics of topological objects. I have tested the idea at the example of a two-dimensional toy model. The results are favorable. In a next step one should go on to the pure SU(3) gauge theory (QCD, ignoring the fermions) in four dimensions. In addition to fine tune known algorithms, it is worthwhile to search for new ones. The so called event-driven algorithm has been proposed a few years ago and has been applied successfully in simulations of condensed matter models. We simulated two-dimensional toy models of QCD by using this algorithm. The performance of the algorithm is convincing. Unfortunately we could not figure out how to apply the algorithm to a gauge theory in four dimensions.
Publications
- Fighting topological freezing in the two-dimensional CPN −1 model, Phys. Rev. D 96, 054504 (2017)
Martin Hasenbusch
(See online at https://doi.org/10.1103/PhysRevD.96.054504) - Exploiting the hopping parameter expansion in the hybrid Monte Carlo (HMC) simulation of lattice QCD with two degenerate flavours of Wilson fermions, Phys. Rev. D 97, 114512 (2018)
Martin Hasenbusch
(See online at https://doi.org/10.1103/PhysRevD.97.114512) - Testing the event-chain algorithm in asymptotically free models, Phys. Rev. D 98, 054502 (2018)
Martin Hasenbusch and Stefan Schaefer
(See online at https://doi.org/10.1103/PhysRevD.98.054502) - Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model, Phys. Rev. E 97, 012119 (2018)
Martin Hasenbusch
(See online at https://doi.org/10.1103/PhysRevE.97.012119)
