The Tunneling Hybrid Monte-Carlo algorithm

Understand

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.