Advances in Lattice Quantum Chromodynamics

In this thesis we make four contributions to the state of the art in numerical lattice simulations of quantum chromodynamics (QCD). First, we present the most detailed investigation yet of the autocorrelations of topological observations in hybrid Monte Carlo simulations of QCD and of the effects of the boundary conditions on these autocorrelations. This results in a numerical criterion for deciding when open boundary conditions are useful for reducing these autocorrelations, which are a major barrier to reliable calculations at fine lattice spacings. Second, we develop a dislocation-enhancing determinant, and demonstrate that it reduces the autocorrelation time of the topological charge. This alleviates problems with slow topological tunneling at fine lattice spacings, enabling simulations on fine lattices to be completed with much less computational effort. Third, we show how to apply the recently developed zMöbius technique to hybrid Monte Carlo evolutions with domain wall fermions, achieving nearly a factor of two speedup in the the light quark determinant, the single most expensive part of the calculation. The dislocation-enhancing determinant and the zMöbius technique have enabled us to begin simulations of fine ensembles with four flavors of dynamical domain wall quarks. Finally, we show how to include the previously-neglected G1 operator in nonperturbative renormalization of the ∆S = 1 effective weak Hamiltonian on the lattice. This removes an important systematic error in lattice calculations of weak matrix elements, in particular the important K → ππ decay.