Topological Charge Evolution in the Markov-Chain of QCD
Derek B. Leinweber, Anthony G. Williams, Jian-bo Zhang (Adelaide), and, Frank X. Lee (GWU, Jlab)
TL;DR
This paper investigates the evolution of topological charge in lattice QCD, proposing a parity transformation method to improve ergodicity and unbiased estimation of topological observables.
Contribution
It introduces a parity transformation technique to enhance sampling of topological sectors in lattice QCD simulations.
Findings
Parity transformation reverses topological charge sign without changing action.
Random application of parity improves ergodicity in Markov-chain sampling.
Enhanced estimator reduces bias in topological charge measurements.
Abstract
The topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological charge and leaves the action invariant. Random applications of the parity transformation are proposed to traverse from one topological charge sign to the other. The transformation provides an improved unbiased estimator of the ensemble average and is essential in improving the ergodicity of the Markov chain process.
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