Domain Wall Fermion QCD with the Exact One Flavor Algorithm

Abstract

Lattice QCD calculations including the effects of one or more non-degenerate sea quark flavors are conventionally performed using the Rational Hybrid Monte Carlo (RHMC) algorithm, which computes the square root of the determinant of ${\mathcal{D}}^{†}\mathcal{D}$, where $\mathcal{D}$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of ${\mathcal{D}}^{†}\mathcal{D}$ --- in particular, no square root is necessary --- enabling a variety of algorithmic developments, which have driven down the cost of simulating the light (up and down) quarks in the isospin-symmetric limit of equal masses. As a result, the relative cost of single quark flavors --- such as the strange or charm --- computed with RHMC has become more expensive. This problem is even more severe in the context of our measurements of the $\Delta I=1/2$ $K\to \pi \pi$ matrix elements on lattice ensembles with $G$-parity boundary conditions, since $G$-parity is associated with a doubling of the number of quark flavors described by $\mathcal{D}$, and thus RHMC is needed for the isospin-symmetric light quarks as well. In this paper we report on our implementation of the exact one flavor algorithm (EOFA) introduced by the TWQCD collaboration for simulations including single flavors of domain wall quarks. We have developed a new preconditioner for the EOFA Dirac equation, which both reduces the cost of solving the Dirac equation and allows us to re-use the bulk of our existing high-performance code. Coupling these improvements with careful tuning of our integrator, the time per accepted trajectory in the production of our 2+1 flavor $G$-parity ensembles with physical pion and kaon masses has been decreased by a factor of 4.2.

61 pages, 18 figures, 14 tables. v2: minor updates for journal submission

References in corpus (6)

• Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
• Standard-model prediction for direct CP violation in $K\to \pi \pi$ decay
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_f=2+1$ Domain Wall QCD
• Gap Domain Wall Fermions
• Lattice QCD with $N_f=2+1+1$ domain-wall quarks

Cited by in corpus (9)

• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Direct CP violation and the $\Delta I=1/2$ rule in $K\to \pi \pi$ decay from the Standard Model
• Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond
• Roper State from Overlap Fermions
• Lattice determination of $I=0$ and 2 $\pi \pi$ scattering phase shifts with a physical pion mass
• Lattice simulations with G-parity Boundary Conditions
• Hessian-free force-gradient integrators
• Numerical stability of force-gradient integrators and their Hessian-free variants in lattice QCD simulations
• 2+1 Flavor Domain Wall Fermion QCD Lattices: Ensemble Production and (some) Properties