An Exact Local Hybrid Monte Carlo Algorithm for Gauge Theories

TL;DR

This paper presents a new local hybrid Monte Carlo algorithm for pure gauge theories that efficiently updates gauge fields using elliptic functions, avoiding numerical integration and enhancing simulation performance.

Contribution

It introduces an exact, local HMC algorithm for gauge theories that employs elliptic functions for classical trajectories, eliminating the need for numerical integration.

Findings

Provides an overrelaxation algorithm with a tunable parameter

Avoids numerical integration of equations of motion

Enhances efficiency of pure gauge theory simulations

Abstract

We introduce a new Monte Carlo method for pure gauge theories. It is not intended for use with dynamical fermions. It belongs to the class of Local Hybrid Monte Carlo (LHMC) algorithms, which make use of the locality of the action by updating individual sites or links by following a classical mechanics trajectory in fictitious time. We choose to update a one-parameter subgroup of the gauge field on each link of the lattice, and the classical trajectory can be found in closed form in terms of elliptic functions for this case. We show that this gives an overrelaxation algorithm with a tunable parameter which, unlike some previous methods, does not require the numerical integration of the equations of motion.