Scaling properties of multiscale equilibration

TL;DR

This paper studies how the equilibration time in a multiscale Monte Carlo algorithm depends on lattice spacing, showing that certain slow modes become less significant as the continuum limit is approached, potentially reducing rethermalization costs.

Contribution

It provides quantitative evidence that the slow modes' impact diminishes at finer lattice spacings, supporting the effectiveness of the multiscale thermalization approach in pure SU(3) gauge theory.

Findings

Slow modes contribute less to rethermalization at finer lattice spacings.

Prolongation operation can produce ensembles indistinguishable from target distributions.

Rethermalization cost may be eliminated at sufficiently fine couplings.

Abstract

We investigate the lattice spacing dependence of the equilibration time for a recently proposed multiscale thermalization algorithm for Markov chain Monte Carlo simulations. The algorithm uses a renormalization-group matched coarse lattice action and prolongation operation to rapidly thermalize decorrelated initial configurations for evolution using a corresponding target lattice action defined at a finer scale. Focusing on non-topological long-distance observables in pure SU(3) gauge theory, we provide quantitative evidence that the slow modes of the Markov process, which provide the dominant contribution to the rethermalization time, have a suppressed contribution toward the continuum limit, despite their associated timescales increasing. Based on these numerical investigations, we conjecture that the prolongation operation used herein will produce ensembles that are indistinguishable from the target fine-action distribution for a sufficiently fine coupling at a given level of statistical precision, thereby eliminating the cost of rethermalization.