Generalized HMC using Nambu mechanics for lattice QCD

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.