Hamiltonian evolution for the hybrid Monte Carlo algorithm

We discuss a class of reversible, discrete approximations to Hamilton's equations for use in the hybrid Monte Carlo algorithm and derive an asymptotic formula for the step-size-dependent errors arising from this family of approximations. For lattice QCD with Wilson fermions, we construct several different updates in which the effect of fermion vacuum polarization is given a longer time step than the gauge field's self-interaction. On a 4⁴ lattice, one of these algorithms with an optimal choice of step size is 30% to 40% faster than the standard leapfrog update with an optimal step size.