Testing and tuning symplectic integrators for the hybrid Monte Carlo algorithm in lattice QCD

We examine a new second-order integrator recently found by Omelyan The integration error of the new integrator measured in the root mean square of the energy difference, (1/2), is about 10 times smaller than that of the standard second-order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increase in cost, the new integrator is about 50% more efficient than the 2LF integrator. Integrating over positions first, then momenta, is slightly more advantageous than the reverse. Further parameter tuning is possible. We find that the optimal parameter for the new integrator is slightly different from the value obtained by Omelyan , and depends on the simulation parameters. This integrator could also be advantageous for the Trotter-Suzuki decomposition in quantum Monte Carlo.