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Register a new userAlgorithms for Dynamical Fermions
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A. D. Kennedy
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This is the write-up of three lectures on algorithms for dynamical fermions that were given at the ILFTN workshop Perspectives in Lattice QCD in Nara during November 2005. The first lecture is on the fundamentals of Markov Chain Monte Carlo methods and introduces the Hybrid Monte Carlo (HMC) algorithm and symplectic integrators; the second lecture covers topics in approximation theory and thereby introduces the Rational Hybrid Monte Carlo (RHMC) algorithm and ways of evading integrator instabilities by means of multiple pseudofermion fields; the third lecture introduces on-shell chiral (Ginsparg-Wilson) lattice fermions and discusses five-dimensional formulations for computing fermion propagators for such fermions.
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We consider recent progress in algorithms for generating gauge field configurations that include the dynamical effects of light fermions. We survey what has been achieved in recent state-of-the-art computations, and examine the trade-offs between performance and control of systematic errors. We briefly review the use of polynomial and rational approximations in Hybrid Monte Carlo algorithms, and some of the theory of on-shell chiral fermions on the lattice. This provides a theoretical framework within which we compare algorithmic alternatives for their implementation; and again we examine the trade-offs between speed and error control.
We summarize four contributions about dynamical twisted mass fermions. The resulting report covers results for N_f=2 obtained from three different gauge actions, namely the standard Wilson plaquette gauge action, the DBW2 and the tree-level Symanzik improved gauge action. In addition, first results for N_f=2+1+1 flavours of twisted mass fermions are discussed.
We report on our study of two-flavor full QCD on anisotropic lattices using $O(a)$-improved Wilson quarks coupled with an RG-improved glue. The bare gauge and quark anisotropies corresponding to the renormalized anisotropy $xi=a_s/a_t = 2$ are determined as functions of $beta$ and $kappa$, using the Wilson loop and the meson dispersion relation at several lattice cutoffs and quark masses.
We perform dynamical QCD simulations with $n_f=2$ overlap fermions by hybrid Monte-Carlo method on $6^4$ to $8^3times 16$ lattices. We study the problem of topological sector changing. A new method is proposed which works without topological sector changes. We use this new method to determine the topological susceptibility at various quark masses.
We report results from full QCD calculations with two flavors of dynamical staggered fermions on anisotropic lattices. The physical anisotropy as determined from spatial and temporal masses, their corresponding dispersion relations, and spatial and temporal Wilson loops is studied as a function of the bare gauge anisotropy and the bare velocity of light appearing in the Dirac operator. The anisotropy dependence of staggered fermion flavor symmetry breaking is also examined. These results will then be applied to the study of 2-flavor QCD thermodynamics.
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