Multi-grid HMC for Ginsparg-Wilson fermions

TL;DR

This paper introduces a multi-grid Hybrid Monte Carlo method that accelerates the generation of Ginsparg-Wilson fermion ensembles by performing most computations on a coarse lattice, significantly reducing computational time.

Contribution

The paper presents a novel multi-grid HMC approach that separates fermion and gauge fields onto different lattice spacings, improving efficiency in lattice QCD simulations.

Findings

Over an order of magnitude reduction in computational time

Most observables computed on the coarse lattice

Efficient conversion between coarse and fine lattices

Abstract

I describe a method that places the fermion fields and the gauge fields on different lattice spacings during the Hybrid Monte Carlo generation of Ginsparg-Wilson dynamical ensembles. The idea is motivated by Wilson's formulation of the renormalisation group. After outlining the underlying theory, I describe a method to perform most of the work of the HMC on a coarse lattice, only requiring to convert to and from the fine lattice once for each independent configuration. Because the bulk of the work takes place on the coarse lattice, including the calculation of most observables, this method saves over an order of magnitude in computer time over previous methods.