Abstract
We show how the integrators used for the molecular dynamics step of the Hybrid Monte Carlo algorithm can be further improved. These integrators not only approximately conserve some Hamiltonian $H$ but conserve exactly a nearby shadow Hamiltonian $\tilde{H}$. This property allows for a new tuning method of the molecular dynamics integrator and also allows for a new class of integrators (force-gradient integrators) which is expected to reduce significantly the computational cost of future large-scale gauge field ensemble generation.
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