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Register a new userDecorrelation of the topological charge in tempered Hybrid Monte Carlo simulations of QCD
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We study the improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering. As an indicator for decorrelation we use the topological charge.
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The improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering is studied. As an indicator for decorrelation the topological charge is used.
The improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering is studied on $10^4$ and $12^4$ lattices. As an indicator for decorrelation the topological charge is used.
The extreme computational costs of calculating the sign of the Wilson matrix within the overlap operator have so far prevented four dimensional dynamical overlap simulations on realistic lattice sizes, because the computational power required to invert the overlap operator, the time consuming part of the Hybrid Monte Carlo algorithm, is too high. In this series of papers we introduced the optimal approximation of the sign function and have been developing preconditioning and relaxation techniques which reduce the time needed for the inversion of the overlap operator by over a factor of four, bringing the simulation of dynamical overlap fermions on medium-size lattices within the range of Teraflop-computers. In this paper we adapt the HMC algorithm to overlap fermions. We approximate the matrix sign function using the Zolotarev rational approximation, treating the smallest eigenvalues of the Wilson operator exactly within the fermionic force. We then derive the fermionic force for the overlap operator, elaborating on the problem of Dirac delta-function terms from zero crossings of eigenvalues of the Wilson operator. The crossing scheme proposed shows energy violations which are better than O($Deltatau^2$) and thus are comparable with the violations of the standard leapfrog algorithm over the course of a trajectory. We explicitly prove that our algorithm satisfies reversibility and area conservation. Finally, we test our algorithm on small $4^4$, $6^4$, and $8^4$ lattices at large masses.
Hasenbusch has proposed splitting the pseudo-fermionic action into two parts, in order to speed-up Hybrid Monte Carlo simulations of QCD. We have tested a different splitting, also using clover-improved Wilson fermions. An additional speed-up between 5 and 20% over the original proposal was achieved in production runs.
We investigate reversibility violations in the Hybrid Monte Carlo algorithm. Those violations are inevitable when computers with finite numerical precision are being used. In SU(2) gauge theory, we study the dependence of observables on the size of the reversibility violations. While we cannot find any statistically significant deviation in observables related to the simulated physical model, algorithmic specific observables signal an upper bound for reversibility violations below which simulations appear unproblematic. This empirically derived condition is independent of problem size and parameter values, at least in the range of parameters studied here.
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