The Tunneling Hybrid Monte-Carlo algorithm

TL;DR

This paper introduces a modified Hybrid Monte-Carlo algorithm that enhances tunneling between topological sectors in lattice QCD simulations by excluding and then correcting for low eigenmodes of the Wilson kernel.

Contribution

It proposes a novel modification to the Hybrid Monte-Carlo algorithm to improve topological tunneling while maintaining high acceptance rates.

Findings

Improved tunneling between topological sectors demonstrated.

Effective suppression of low eigenmodes without compromising acceptance rate.

Potential for more efficient lattice QCD simulations.

Abstract

The hermitian Wilson kernel used in the construction of the domain-wall and overlap Dirac operators has exceptionally small eigenvalues that make it expensive to reach high-quality chiral symmetry for domain-wall fermions, or high precision in the case of the overlap operator. An efficient way of suppressing such eigenmodes consists of including a positive power of the determinant of the Wilson kernel in the Boltzmann weight, but doing this also suppresses tunneling between topological sectors. Here we propose a modification of the Hybrid Monte-Carlo algorithm which aims to restore tunneling between topological sectors by excluding the lowest eigenmodes of the Wilson kernel from the molecular-dynamics evolution, and correcting for this at the accept/reject step. We discuss the implications of this modification for the acceptance rate.