Topological tunnelling with dynamical overlap fermions

Tunnelling between different topological sectors with dynamical chiral fermions is difficult because of a poor mass scaling of the pseudo-fermion estimate of the determinant. For small fermion masses it is virtually impossible using standard methods. However, by projecting out the small Wilson eigenvectors from the overlap operator, and treating the correction determinant exactly, we can significantly increase the rate of topological sector tunnelling and reduce substantially the auto-correlation time. We present and compare a number of different approaches, and advocate a method which allows topological tunnelling even at low mass with little addition to the computational cost.