Modifying the molecular dynamics action to increase topological tunnelling rate for dynamical overlap fermions

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.