Domain Wall Fermion Simulations with the Exact One-Flavor Algorithm

TL;DR

This paper presents the implementation and optimization of the exact one-flavor algorithm (EOFA) for domain wall fermion simulations, demonstrating it is significantly faster than the traditional RHMC method for simulating single quark flavors.

Contribution

The authors independently implemented EOFA in CPS and BFM, optimized it with a novel preconditioning technique, and validated its efficiency and equivalence to RHMC in lattice QCD simulations.

Findings

EOFA is 2.4 times faster than RHMC per trajectory.

Implementation of EOFA in CPS and BFM was successful and validated.

Further optimization and retuning could improve EOFA performance.

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 M\"{o}bius 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 $N_{f} = 2+1$ M\"{o}bius 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.