Minimal Autocorrelation in Hybrid Monte Carlo simulations using Exact Fourier Acceleration

TL;DR

This paper introduces an exact Fourier acceleration method that significantly reduces autocorrelation times in hybrid Monte Carlo simulations by addressing key sources of autocorrelation, improving efficiency across various physical models.

Contribution

The work presents analytic solutions and implementation of the exact Fourier acceleration method to eliminate autocorrelations in HMC, applicable to actions with quadratic components.

Findings

Autocorrelation reduced by multiple orders of magnitude.

Effective for near-harmonic potentials and various models.

Improves efficiency of HMC simulations.

Abstract

The hybrid Monte Carlo (HMC) algorithm is a ubiquitous method in computational physics with applications ranging from condensed matter to lattice QCD and beyond. However, HMC simulations often suffer from long autocorrelation times, severely reducing their efficiency. In this work two of the main sources of autocorrelations are identified and eliminated. The first source is the sampling of the canonical momenta from a sub-optimal normal distribution, the second is a badly chosen trajectory length. Analytic solutions to both problems are presented and implemented in the exact Fourier acceleration (EFA) method. It completely removes autocorrelations for near-harmonic potentials and consistently yields (close-to-) optimal results for numerical simulations of the Su-Schrieffer-Heeger and the Ising models as well as in lattice gauge theory, in some cases reducing the autocorrelation by multiple orders of magnitude. EFA is advantageous for and easily applicable to any HMC simulation of an action that includes a quadratic part.