Trivializing maps, the Wilson flow and the HMC algorithm

TL;DR

This paper explores the use of trivializing maps generated by the Wilson flow to enhance the efficiency of Hybrid Monte Carlo simulations in lattice QCD by decoupling field variables.

Contribution

It introduces a systematic method to construct trivializing maps via flow equations and proposes combining the Wilson flow with HMC to improve simulation performance.

Findings

Wilson flow generates approximately trivializing maps for the Wilson gauge action

Combining Wilson flow with HMC can potentially improve lattice QCD simulation efficiency

The construction of trivializing maps is detailed and systematically developed

Abstract

In lattice gauge theory, there exist field transformations that map the theory to the trivial one, where the basic field variables are completely decoupled from one another. Such maps can be constructed systematically by integrating certain flow equations in field space. The construction is worked out in some detail and it is proposed to combine the Wilson flow (which generates approximately trivializing maps for the Wilson gauge action) with the HMC simulation algorithm in order to improve the efficiency of lattice QCD simulations.