Topology, the Wilson flow and the HMC algorithm

Abstract

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.

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)

References in corpus (1)

• Finite volume QCD at fixed topological charge

Cited by in corpus (15)

• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Review of lattice results concerning low energy particle physics
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Critical slowing down and error analysis in lattice QCD simulations
• Lattice QCD with open boundary conditions and twisted-mass reweighting
• The lattice gradient flow at tree-level and its improvement
• Space-time symmetries and the Yang-Mills gradient flow
• Remarks on strange-quark simulations with Wilson fermions
• Extended investigation of the twelve-flavor $\beta$-function
• Testing trivializing maps in the Hybrid Monte Carlo algorithm
• Topological susceptibility in lattice Yang-Mills theory with open boundary condition
• Wilson fermions at fine lattice spacings: scale setting, pion form factors and (g-2)_mu
• Open Boundary Condition, Wilson Flow and the Scalar Glueball Mass
• Physical observables from boundary artifacts: scalar glueball in Yang-Mills theory
• Non-abelian lattice gauge theory with a topological action