Speeding up the Hybrid-Monte-Carlo algorithm for dynamical fermions

TL;DR

The paper addresses the rising computational cost of dynamical-fermion simulations as the sea-quark mass nears the chiral limit. It introduces a simple split of the pseudo-fermion action using a second, lighter matrix to reduce condition numbers and permit larger integration steps at the same acceptance. In a two-dimensional Schwinger model with Wilson fermions and even-odd preconditioning, the approach yields significant speedups—up to about twofold in the tested regime—while preserving physical observables. The modification is easy to implement in existing HMC codes and holds promise for improving lattice QCD efficiency, with potential extensions to higher-dimensional theories and PHMC variants.

Abstract

We propose a modification of the Hybrid-Monte-Carlo algorithm that allows for a larger step-size of the integration scheme at constant acceptance rate. The key ingredient is that the pseudo-fermion action is split into two parts. We test our proposal at the example of the two-dimensional lattice Schwinger model with two degenerate flavours of Wilson-fermions.