Worldvolume Hybrid Monte Carlo algorithm for group manifolds

Abstract: The Worldvolume Hybrid Monte Carlo (WV-HMC) method [arXiv:2012.08468] is a reliable and versatile algorithm for addressing the sign problem. It resolves the ergodicity issues commonly encountered in Lefschetz thimble-based approaches at a low computational cost. In this article, as a first step toward applying WV-HMC to lattice QCD, we extend the algorithm to cases where the configuration space is a group manifold. The key idea is to formulate the algorithm using a phase-space integral over the tangent bundle of the worldvolume, which naturally carries a symplectic structure. The validity of this novel algorithm is demonstrated using the one-site model with a purely imaginary coupling constant.