Higher-order hybrid Monte Carlo algorithms

We present a simple recursive iteration of the leapfrog discretization of Newton’s equations which leads to a removal of the finite-step-size error to any desired order. This is done in a manner that preserves phase-space areas and reversibility, as required for use in the hybrid Monte Carlo method for simulating fermionic fields. The resulting asymptotic volume dependence is exp[(lnV${)}^{1/2}$]. We test the scheme on the (2+1)-dimensional Hubbard model.