Algorithms for Dynamical Fermions

TL;DR

This paper provides an overview of algorithms for simulating dynamical fermions in lattice QCD, focusing on HMC, RHMC, and chiral fermion formulations, with insights into their theoretical foundations and computational techniques.

Contribution

It introduces and explains advanced algorithms like RHMC and discusses five-dimensional formulations for chiral fermions, enhancing computational methods in lattice QCD.

Findings

Hybrid Monte Carlo algorithm fundamentals explained

Rational Hybrid Monte Carlo algorithm and pseudofermion techniques discussed

Five-dimensional formulations for chiral fermions introduced

Abstract

This is the write-up of three lectures on algorithms for dynamical fermions that were given at the ILFTN workshop 'Perspectives in Lattice QCD' in Nara during November 2005. The first lecture is on the fundamentals of Markov Chain Monte Carlo methods and introduces the Hybrid Monte Carlo (HMC) algorithm and symplectic integrators; the second lecture covers topics in approximation theory and thereby introduces the Rational Hybrid Monte Carlo (RHMC) algorithm and ways of evading integrator instabilities by means of multiple pseudofermion fields; the third lecture introduces on-shell chiral (Ginsparg-Wilson) lattice fermions and discusses five-dimensional formulations for computing fermion propagators for such fermions.