Critical slowing down and error analysis in lattice QCD simulations

TL;DR

This paper investigates the severe critical slowing down in lattice QCD simulations, especially for topological charge, and proposes a method to improve error analysis by accounting for slow modes.

Contribution

It provides a detailed analysis of critical slowing down in lattice QCD and introduces a new approach to incorporate slow mode information into error estimates.

Findings

Critical slowing down for topological charge has an effective exponent of about 5.

Wilson loops decouple from slow modes, reducing their impact.

The proposed method improves the reliability of error estimates in simulations.

Abstract

We study the critical slowing down towards the continuum limit of lattice QCD simulations with Hybrid Monte Carlo type algorithms. In particular for the squared topological charge we find it to be very severe with an effective dynamical critical exponent of about 5 in pure gauge theory. We also consider Wilson loops which we can demonstrate to decouple from the modes which slow down the topological charge. Quenched observables are studied and a comparison to simulations of full QCD is made. In order to deal with the slow modes in the simulation, we propose a method to incorporate the information from slow observables into the error analysis of physical observables and arrive at safer error estimates.