Improvement in Autocorrelation Times Measured by the Master-Field Technique using Field Transformation HMC in 2+1 Domain Wall Fermion Simulations

TL;DR

This paper demonstrates that applying a field transformation within the Hybrid Monte Carlo algorithm reduces autocorrelation times in 2+1 domain wall fermion simulations, improving efficiency in measuring infrared observables.

Contribution

It introduces a novel field transformation inspired by Wilson flow to the HMC algorithm, effectively reducing autocorrelation times in lattice QCD simulations.

Findings

Reduction in autocorrelation times for Wilson-flowed energy densities

Decreased autocorrelation for topological charge densities

Effective estimation of autocorrelation improvements with fewer configurations

Abstract

The Field-Transformation Hybrid Monte-Carlo (FTHMC) algorithm potentially mitigates the issue of critical slowing down by combining the HMC with a field transformation, originally proposed by L\"{u}scher and motivated as trivializing the theory. For the transformation, we use a single invertible discrete smearing step inspired by the Wilson flow but which resembles a Jacobian-computable generalisation of the stout smearing step. This is applied to a system with Iwasaki gauge fields and 2+1 Domain-Wall fermions. We have studied the effect of different smearing parameter values on autocorrelation times of Wilson-flowed energies with different flow time. We have found a reduction of exponential autocorrelation times for infra-red observables such as Wilson flowed energy densities and topological charge densities when a larger value of the smearing parameter is used. The autocorrelation times of local observables are computed using an approach akin to the master-field technique, allowing us to estimate the effect of the field transformation with different parameters based on a small number of configurations.