Multi-grid HMC for Ginsparg-Wilson fermions

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.