Generalized HMC using Nambu mechanics for lattice QCD

TL;DR

This paper introduces a generalized hybrid Monte Carlo algorithm using Nambu mechanics, enabling more efficient lattice QCD simulations by incorporating non-local forces and potentially reducing critical slowing down.

Contribution

The paper presents a novel HMC extension with Nambu dynamics that includes non-local forces, improving sampling efficiency in lattice QCD.

Findings

Allows inclusion of non-local forces in MD steps

Preserves the target probability distribution

Potentially reduces critical slowing down

Abstract

I describe a generalization of the hybrid Monte Carlo (HMC) algorithm in which the molecular dynamics (MD) steps utilize Nambu generalized Hamiltonian dynamics. Characterized by multiple Hamiltonian functions, this formalism allows me to include forces from non-local objects in the MD evolution while preserving the target probability distribution. In this way, the changes proposed by the MD at one location can be made using instantaneous knowledge of the long-distance behavior of the gauge field to a degree beyond that usually provided by the fermion determinant. This represents a promising method for reducing critical slowing down in lattice QCD simulations.