  We describe a new Hybrid Monte Carlo (HMC) algorithm for dynamical overlap
fermions, which improves the rate of topological index changes by adding an
additional (intensive) term to the action for the molecular dynamics part of
the algorithm. The metropolis step still uses the exact action, so that the
Monte Carlo algorithm still generates the correct ensemble. By tuning this new
term, we hope to be able to balance the acceptance rate of the HMC algorithm
and the rate of topological index changes. We also describe how suppressing,
but not eliminating, the small eigenvalues of the kernel operator may improve
the volume scaling of the cost per trajectory for overlap HMC while still
allowing topological index changes.
  We test this operator on small lattices, comparing our new algorithm with an
old overlap HMC algorithm with a slower rate of topological charge changes, and
an overlap HMC algorithm which fixes the topology. Our new HMC algorithm more
than doubles the rate of topological index changes compared to the previous
state of the art, while maintaining the same metropolis acceptance rate. We
investigate the effect of topological index changes on the local topological
charge density, measured using an improved field theoretic operator after heavy
smearing. We find that the creation and annihilation of large lumps of
topological charge is increased with the new algorithm.
