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تسجيل مستخدم جديدOne-flavor algorithm for Wilson and domain-wall fermions
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We construct positive-definite pseudofermion actions for one fermion flavor in lattice field theory, for Wilson and domain-wall fermions respectively. The positive definiteness of these actions ensures that they can be simulated with the Hybrid Monte Carlo (HMC) method. For lattice QCD with optimal domain-wall quarks, we compare the efficiency of HMC simulations of 2-flavor and (1+1)-flavor, and find that the efficiency ratio is about 3:2.
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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 $mathscr{D}^{dagg
er} mathscr{D}$, where $mathscr{D}$ is the Dirac operator. The special case of two degenerate quark flavors with the same mass is described directly by the determinant of $mathscr{D}^{dagger} mathscr{D}$ --- 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 $Delta I = 1/2$ $K rightarrow pi pi$ 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 $mathscr{D}$, 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.
We present an exact dynamical QCD simulation algorithm for the $O(a)$-improved Wilson fermion with odd number of flavors. Our algorithm is an extension of the non-Hermitian polynomials HMC algorithm proposed by Takaishi and de Forcrand previously. In
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