Domain Wall Fermion Simulations with the Exact One-Flavor Algorithm

Abstract

As algorithmic developments have driven down the cost of simulating degenerate light quark flavors the relative cost of simulating single quark flavors with the Rational Hybrid Monte Carlo (RHMC) algorithm has become more expensive. TWQCD has proposed an exact one-flavor algorithm (EOFA) that allows for HMC simulations of a single quark flavor without taking a square root of the fermion determinant. We have independently implemented EOFA in the Columbia Physics System (CPS) and BAGEL Fermion Sparse-Matrix Library (BFM) for Shamir and Möbius domain wall fermions, and begun to optimize and test our implementation against RHMC. In this talk we discuss the derivation of the EOFA action, our tests of its equivalence to RHMC, and the current state of our implementation and optimization. We find, after introducing a novel preconditioning technique for the EOFA Dirac operator, that EOFA is a factor of 2.4 times faster than RHMC per molecular dynamics trajectory for the strange quark determinant on an $N_{f} = 2+1$ Möbius DWF ensemble with physical quark masses and a $24^{3} \times 64 \times 24$ volume. We expect that further improvement is possible by retuning the integrator parameters for EOFA and by continuing to optimize our code.