  The hermitian Wilson kernel used in the construction of the domain-wall and
overlap Dirac operators has exceptionally small eigenvalues that make it
expensive to reach high-quality chiral symmetry for domain-wall fermions, or
high precision in the case of the overlap operator. An efficient way of
suppressing such eigenmodes consists of including a positive power of the
determinant of the Wilson kernel in the Boltzmann weight, but doing this also
suppresses tunneling between topological sectors. Here we propose a
modification of the Hybrid Monte-Carlo algorithm which aims to restore
tunneling between topological sectors by excluding the lowest eigenmodes of the
Wilson kernel from the molecular-dynamics evolution, and correcting for this at
the accept/reject step. We discuss the implications of this modification for
the acceptance rate.
