An old and apparently persistent problem in numerical lattice QCD is that the simulations tend to get trapped in a sector of fixed topological charge when the lattice spacing is taken to zero. The effect sets in very rapidly and may invalidate the simulation results in certain cases. In this talk, the issue is discussed using the Wilson flow as a tool. The flow has a simple scaling behaviour and allows one to understand how exactly the topological sectors emerge in the continuum limit. Further studies however suggest that the observed slowdown of the simulations at small lattice spacings is only partly caused by the emergence of the sectors.
@article{arxiv.1009.5877,
title = {Topology, the Wilson flow and the HMC algorithm},
author = {Martin Lüscher},
journal= {arXiv preprint arXiv:1009.5877},
year = {2014}
}
Comments
LaTeX source, 13 pages, 6 figures. Talk given at the XXVIII International Symposium on Lattice Field Theory, June 14-19 2010, Villasimius, Italy. Corrected figures 4 and 5, following the discovery of a bug in the analysis programs (thanks to Yoshifumi Nakamura)