Topology, the Wilson flow and the HMC algorithm

TL;DR

This paper investigates the emergence of topological sectors in lattice QCD simulations using the Wilson flow, revealing insights into simulation slowdown at small lattice spacings and its implications for accurate results.

Contribution

It introduces the Wilson flow as a tool to understand topological sector emergence and analyzes its role in the slowdown of simulations at fine lattice spacings.

Findings

Wilson flow exhibits simple scaling behavior

Topological sectors emerge in the continuum limit

Simulation slowdown is only partly due to topological sector emergence

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.