Worldvolume Hybrid Monte Carlo algorithm for group manifolds

TL;DR

The paper extends the Worldvolume Hybrid Monte Carlo algorithm to systems on compact group manifolds, improving ergodicity and computational efficiency in lattice gauge theories.

Contribution

It introduces a symplectic structure on the tangent bundle for WV-HMC, enabling its application to group manifolds in lattice gauge theories.

Findings

Validated the algorithm with a one-site model with imaginary coupling.

Resolved ergodicity issues in Lefschetz thimble approaches.

Maintained low computational costs.

Abstract

The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the numerical sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based approaches while maintaining low computational costs. In this paper, as a general framework for applying WV-HMC to lattice gauge theories, we extend the algorithm to systems defined on compact group manifolds. The key is to introduce a symplectic structure on the tangent bundle of the worldvolume and formulate molecular dynamics upon it. The validity of the proposed algorithm is demonstrated using the one-site model with a purely imaginary coupling constant.