Title:

The rational hybrid Monte Carlo algorithm

This thesis is concerned with the problem of generating gauge configurations for use with Monte Carlo lattice QCD calculations that include the effect of dynamical fermions. Although such effects have been included in calculations for a long time, historically it has been difficult to include the effect of the strange quark because of the square root of the Dirac operator that appears in the action. The lattice formulation of QCD is discussed, and the various fermion formulations are highlighted. Current popular algorithms used to generate gauge configurations are described, in particular the advantages and disadvantages of each are discussed. The Rational Hybrid Monte Carlo algorithm (RHMC) is introduced, this uses rational functions to approximate the matrix square root and is an exact algorithm. RHMC is compared with the Polynomial Hybrid Monte Carlo algorithm and the inexact R algorithm for two flavour staggered fermion calculations. The algorithm is found to reproduce published data and to be more efficient than the Polynomial Hybrid Monte Carlo algorithm. With the introduction of multiple time scales for the gauge and fermion parts of the action the efficiency further increases. As a means to accelerate the Monte Carlo acceptance rate of lattice QCD calculations, the splitting of the fermion determination into n^{th} root contributions is described. This is shown to improve the conservation of the Hamiltonian. As the quark mass is decreased this is found to decrease the overall cost of calculation by allowing an increase in the integrating stepsize. An efficient formulation for applying RHMC to ASQTAD calculations is described, and it is found to be no more expensive than using the conventional R algorithm formulation. Full 2+1 quark flavour QCD calculations are undertaken using the domain wall fermion formulation. Results are generated using both RHMC and the R algorithm and comparisons are made on the basis of algorithm efficiency and hadronic observables. With the exception of the stepsize errors present in the R algorithm data, consistency is found between the two algorithms. RHMC is found to allow a much greater integrating stepsize than the R algorithm.
