Topology changing update algorithms for lattice QCD simulations

• Applicant: Professor Christian Hölbling, Ph.D.
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 545079884

Lattice quantum chromodynamics (lattice QCD) is the primary method to obtain quantitative predictions in the low energy sector of the strong nuclear force. The fundamental theory describing the strong nuclear interaction between quarks, QCD, is discretized on a space-time lattice and solved numerically using supercomputers. To minimise systematic errors in applications such as the search for new physics on the precision frontier, the elucidation of the proton structure, or the prediction of thermodynamic properties of nuclear matter, it is imperative to reduce the discretization scale, the so-called lattice spacing. However, straightforward efforts to reduce the lattice spacing while maintaining to use standard algorithms are thwarted by the topological structure of QCD, or, more precisely, the topological structure of the gluon fields contained in QCD. As one reduces the lattice spacing, barriers form between different topological sectors, leaving conventional update algorithms stuck, with only a subset of the relevant field configurations reachable by the algorithm. This problem is known as topological freezing. We have recently proposed and implemented a new algorithm, which was able to break through the topological barriers in a theory with gauge fields alone, in a region, where all conventional algorithms fail. This algorithm requires minimal overhead, does not reduce the effective sample size and is straightforward to implement for full QCD. In this project, we will implement and test this algorithm in full QCD. We will further study potential improvements of our method and possible synergies with machine learning and more classical techniques to speed up the generation of independent gauge ensembles. We will look at first phenomenological applications and provide an open source code as reference for the community.

• DFG Programme: Research Grants